## Séminaire d’Analyse Fonctionnelle

publié le , mis à jour le

Le séminaire a lieu le mardi à 13h45, en salle 316Bbis du bâtiment de
Métrologie (plan d’accès). Pour le moment, nous alternons des exposés virtuels (pour le lien, contactez la responsable) et classiques.

Vous trouverez ci-dessous le planning du séminaire d’Analyse
Fonctionnelle pour l’année universitaire en cours.
L’historique des séminaires des années précédentes se trouve
ici.

Pour contacter le responsable (Tony Prochazka) : antonin.prochazka univ-fcomte.fr.
Pour s’abonner au séminaire : ACM.

### Exposés à venir

-Mardi 11 mai: Fabio Cipriani, Politecnico di Milano
(en ligne) On a noncommutative Sierpiński gasket

We illustrate the construction of a C*-algebra A that can be genuinely interpreed as a quantization of the classical Sierpiński gasket, the most studied instance of a self-similar fractal space. We further describe the discrete and continuous spectrum of A, the structure of the traces on A as well as the construction of a Dirichlet form E and of a spectral triple (A,D,H).

-Mardi 25 mai: David Kyed, University of Southern Denmark, Odense
(en ligne) The Podleś spheres converge to the sphere

The Podleś spheres, which are q-deformed analogues of the 2-sphere, are by now among the most classical objects in non-commutative geometry, but only recently their structure as non-commutative Riemannian manifolds has begun to unravel. In my talk, I will first provide an introduction to Rieffel’s notion of compact quantum metric spaces and his non-commutative counterpart to the Gromov-Hausdorff distance, and then present some recent progress within this field which shows that the quantised 2-spheres actually converge (in the quantum Gromov-Hausdorff distance) to the classical round 2-sphere as the deformation parameter q tends to 1. The talk is based on joint works with Konrad Aguilar and Jens Kaad.

-Mardi 8 juin: Haonan Zhang, IST Austria
(en ligne) Curvature-dimension conditions for symmetric quantum Markov semigroups

The curvature-dimension condition consists of the lower Ricci curvature bound and upper dimension bound of the Riemannian manifold, which has a number of geometric consequences and is very helplful in proving many functional inequalities. In this talk I will speak about two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet-Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz-Schur multipliers over group algebras and depolarizing semigroups. Joint work with Melchior Wirth (IST Austria).

## Avril

• Mardi 27 avril : Loris Arnold, LMB

## Mars

• Mardi 9 mars : Ryosuke Sato, Nagoya University
(en ligne)
Markov dynamics on unitary duals of compact quantum groups

In this talk, we will discuss Markov semigroups on unitary duals (i.e., the set of all irreducible representations) of compact quantum groups. First, we will construct quantum Markov semigroups on the group von Neumann algebra of compact quantum group based on its Hopf-algebra structure and characters of the compact quantum group. Then we will show the dynamics preserve the center of the group von Neumann algebra, and it gives the dynamics on the unitary dual. Moreover, the dynamics have generators, and we can describe it explicitly by the representation theory. In particular, we will deal with the case of quantum unitary groups.

• Mardi 16 mars : Gilles Lancien, LMB
Plongements non linéaires dans les duaux séparables

Le théorème d’Aharoni (1974) assure que tout espace métrique séparable se plonge de façon bi-Lipschitz dans $c_0$. C’est une question ouverte importante de savoir si tout Banach contenant une copie bi-Lipschitz de $c_0$ contient un sous-espace linéairement isomorphe à $c_0$. Dans cet exposé nous considérerons des questions similaires en relation avec la notion plus faible de plongement grossier. Dans un papier publié en 2007, un grand pas a été fait par N. Kalton, qui a prouvé qu’un Banach contenant grossièrement $c_0$ ne peut pas être réflexif. Cependant, on ignore encore si un tel espace peut être un dual separable. Dans cet exposé, nous discuterons de certains aspects de cette question. L’argument de Kalton est basé sur l’utilisation de graphes métriques particuliers, dits entrelacés’’. Nous donnerons des résultats sur les duaux contenant de façon équi-Lipschitz ou équi-grossière ces graphes, en relation avec leur indice de Szlenk et nous prouverons leur optimalité.
Travail en commun avec B. de Mendonça Braga, C. Petitjean and A. Procházka.

• Mardi 30 mars : Hua Wang, LMB
Exemples de biproduits croisés ayant propriété (RD)

Je vais d’abord parler rapidement la propriété (RD) pour les groupes
quantiques discrets de type Kac et dire quelques mots comme motivation. Puis
je vais présenter un critère pour voir si les biproduits croisés possèdent
cette propriété. Enfin, je vais introduire une procédure pour construire
explicitement exemples de biproduits croisés ayant ou sans cette propriété,
et parler la limitation de cette procédure.

## Février

• Mardi 23 février à 16h00 : Michael Brannan, Texas A&M University
(en ligne)
Complete logarithmic Sobolev inequalities and non-commutative Ricci curvature

I will give a brief introduction to the study of log-Sobolev type inequalities (LSI’s) for quantum Markov semigroups and some of their applications. In the context of classical heat semigroups on compact Riemannian manifolds, the famous Bakry-Emery theorem provides a beautiful connection between the geometry of the underlying manifold and the LSI, showing that a positive lower bound on the Ricci curvature implies an LSI for the heat semigroup. I will discuss an information-theoretic approach to obtain modified log-Sobolev inequalities based on non-positive non-commutative Ricci curvature lower bounds previously developed by Carlen and Maas. Using these tools, we are able to find new examples of quantum Markov semigroups satisfying a completely bounded version of the modified LSI, including heat semigroups on free quantum groups. This talk is based on joint work with Li Gao (TUM) and Marius Junge (UIUC).

## Janvier

• Mardi 12 janvier à 13h45 : Marek Bożejko, University of Wrocław
Remarks on Generalized Gaussian processes and positive
definite functions on some Coxeter groups

In my talk I will present the following topics :
1. Strong connections between generalized Gaussian processes and some class of positive definite functions on permutations group.
2. Type B Fock spaces and new Gaussian processes of type B , relations with q-Meixner-Pollaczek polynomials and Meixner probability measures like 1/cosh.
3. Thoma repsentation of central positive definite functions on Coxeter groups of type A and B and new classes of generalized Gaussian processes.
4. Open problems.

## Novembre

• Mardi 3 novembre à 13h30 : Tony Prochazka, LMB
Compact reduction in Lipschitz-free spaces

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. The main new results are : ℱ(X) is weakly sequentially complete for every superreflexive Banach space X, and ℱ(M) has the Schur property and the approximation property for every scattered complete metric space M. This is a joint work with R. Aliaga, C. Noûs and C. Petitjean.

## Octobre

• Mardi 6 octobre, 13:45 : Jean-Christophe Bourin, LMB
Une décomposition pour les matrices partitionnées

On établit "un théorème de Pythagore" pour les matrices partitionnées qui entraîne de nombreuses inégalités.

• Mardi 20 octobre, 13:45 (en ligne) : Jonas Wahl, Hausdorff Center for Mathematics, Bonn
Markov dynamics on branching graphs of diagram algebras

Thoma’s famous theorem on the classification of characters on
the infinite symmetric group has been very influential in different
areas of mathematics such as combinatorics and probability theory. In
this talk, we explain versions of Thoma’s theorem for different diagram
algebras arising out of subfactor theory and Banica and Speicher’s
theory of easy quantum groups. As Thoma’s classical theorem, these
results can be formulated in a probabilistic language and we find
interesting new connections to random lattice paths and random walks on
trees.

## Septembre

• Mardi 8 septembre, 13:30 (en ligne) : Jacek Krajczok, IMPAN, Warsaw
Type I locally compact quantum groups : coamenability and
applications

We say that a locally compact quantum group is type I if its
universal C* algebra (which is equal to $C^u_0(\hatG)$) is type I.
This class of quantum groups can be though of as an intermediate step
between compact and general locally compact quantum groups ; they are
significantly more general than compact ones, but still have tractable
representation theory. Similarly to the compact case, one can define
"character-like" operators associated with suitable representations. I
will discuss a result which states that coamenability of G is equivalent
to a certain condition on spectra of these operators. If time permits, I
will also discuss how one can use theory of type I locally compact
quantum groups to show that the quantum space underlying the Toeplitz
algebra does not admit a quantum group structure (joint work with Piotr
Sołtan).

• Mardi 22 septembre, 13:45 (en ligne) : Biswarup Das, Wroclaw University
Towards quantizing separate continuity : A quantum version of Ellis joint continuity theorem

Let S be a topological space, which is also a semigroup with identity, such that the multiplication is separately continuous. Such semigroups are called semitopological semigroups. These type of objects occur naturally, if onestudies weakly almost periodic compactification of a topological group. Now if we assume the following : (a) The topology of S is locally compact. (b) Abstract algebraically speaking, S is a group (i.e. every element has an inverse). (c) The multiplication is separately continuous as above (no other assumption. This is the only assumption concerning the interaction of the topology with the group structure). Then it follows that S becomes a topological group i.e. : (a) The multiplication becomes jointly continuous. (b) The inverse is also continuous. This extremely beautiful fact was proven by R. Ellis in 1957 and is known in the literature as Ellis joint continuity theorem. In this talk, we will prove a non-commutative version of this result. Upon briefly reviewing the notion of semitopological semigroup, we will introduce ’’compact semitopological quantum semigroup’’ which were before introduced by M. Daws in 2014 as a tool to study almost periodicity of Hopf von Neumann algebras. Then we will give a necessary and sufficient condition on these objects, so that they become a compact quantum group. As a corollary, we will give a new proof of the Ellis joint continuity theorem as well. This is the joint work with Colin Mrozinski.

• Mardi 29 septembre, 13:45, salle 316B : Uwe Franz, LMB
Quelques applications de la cohomologie de Hochschild aux probabilités non commutatives

Les semi-groupes de convolution d’états sur un espace de probabilités non commutatif sont en général caractérisés par leur dérivée en t=0, qu’en appelle leur fonctionnelle génératrice. Une telle fonctionnelle $\psi$ peut être complétée en un triplet $(\rho,\eta,\psi)$, dont les composantes sont caractérisées par des relations cohomologiques. Dans mon expose je vais rappeler la cohomologie de Hochschild ainsi que cette construction. Ensuite nous allons regarder quelques applications du premier et deuxième groupes de cohomologie à l’étude des fonctionnelles génératrices.

## Agenda

• ### Mardi 12 octobre 13:45-14:45 - Guillaume Grelier - Universidad de Murcia

Extremal structure in ultrapowers of Banach spaces

Résumé : Given a bounded convex subset $C$ of a Banach space $X$ and a free ultrafilter $\mathcal U$, we study which points $(x_i)_\mathcal U$ are extreme points of the ultrapower $C_\mathcal U$ in $X_\mathcal U$. In general, we obtain that when $(x_i)$ is made of extreme points (respectively denting points, strongly exposed points) and they satisfy some kind of uniformity, then $(x_i)_\mathcal U$ is an extreme point (respectively denting point, strongly exposed point) of $C_\mathcal U$. We also show that extreme points and strongly extreme points of $C_\mathcal U$ coincide provided $\mathcal U$ is a countably incomplete ultrafilter. Finally, we analyse the extremal structure of $C_\mathcal U$ in the case that $C$ is a super weakly compact or uniformly convex set. Joint work with L. C. García-Lirola and A. Rueda Zoca.

Lieu : 316Bbis

• ### Mardi 19 octobre 13:45-14:45 - Eric Ricard - Université de Caen

Inégalités pour des anticommutateurs.

Résumé : Je vais présenter plusieurs inégalités qui permettent de terminer l’étude du module de continuité des applications de Mazur entre Lp-non commutatifs pour des indices plus petits que 1. Elles sont intimement liées aux inégalités de Khintchine non commutatives et permettent d’en donner une preuve simple.

Lieu : 316Bbis

• ### Mardi 19 octobre 15:00-16:00 - Janusz Wysoczański - Uniwersytet Wrocławski

Joint monotone and boolean numerical and spectral radii of d-tuples of operators

Lieu : 316Bbis

• ### Mercredi 20 octobre 13:45-14:45 - Anna Wysoczańska-Kula - Uniwersytet Wrocławski

Does Levy-Khinchine decomposition exists in the noncommutative framework ?

Résumé : Known since 1930ies, the Lévy-Khintchine formula provides a classification of Lévy processes on $\mathbb R^n$ in terms of their generators. It shows how the generators of Lévy processes are combinations of continuous (or Gaussian) parts and jump parts. In my talk I will discuss the problem of the existence of an analogous decomposition for Lévy processes’ generators on $*$-bialgebras and compact quantum groups, and comment on recent developments in this area.

Lieu : 309B

• ### Mardi 26 octobre 13:45-14:45 - Matias Raja - Universidad de Murcia

Uniformly convex functions and applications

Résumé : The notion of uniform convexity for functions was introduced by Levitin and Polyak in the 60′s, that localises in a certain way some good properties of functions defined on uniformly convex spaces. Since then, the properties of uniformly convex functions have been studied by several authors, notably Vladimirov, Nesterov, Chekanov, Zaˇlinescu, Borwein, Vanderwerff, Guirao and Hájek.
Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key for further constructions.
We will provide two applications of our results and techniques in this talk. Firstly, we will show how Enflo’s uniformly convex renorming of super-reflexive spaces can be retrieved in a quite natural way.
The second application is related to the notion of super weakly compactness. After a brief overview of the state of the art on this topic, we will discuss several fashions to quantify the non-super weakly compactness of a subset of a Banach space and then we will prove that they all are equivalent.
This is a joint work with G. Grelier recently published in JMAA.

Lieu : 316Bbis

• ### Mardi 9 novembre 13:45-14:45 - Louis Labuschagne - North-West University

Von Neumann algebra conditional expectations with applications to generalized representing measures for noncommutative function algebras

Résumé : We establish several deep existence criteria for conditional expectations on von Neumann algebras, and then apply this theory to develop a noncommutative theory of representing measures of characters of a function algebra. Our main cycle of results describes what may be understood as a noncommutative Hoffman-Rossi theorem’ giving the existence of weak* continuous noncommutative representing measures’ for so-called $D$-characters. These results may also be viewed as module’ Hahn-Banach extension theorems for weak* continuous characters’ into possibly noninjective von Neumann algebras. In closing we introduce the notion of `noncommutative Jensen measures’, and show that as in the classical case representing measures of logmodular algebras are Jensen measures.

Lieu : 316Bbis

• ### Mardi 23 novembre 13:45-14:45 - Bernhard Haak - Université de Bordeaux

Observabilité exacte pour des groupes continues et discrets

Résumé : Dans cet exposé nous nous intéressons à l’observabilité exacte de groupes bornés sur un espace de Hilbert ou de Banach, soit dans un cadre discret, soit dans un cadre continu. L’analyse commence avec un analogue discret du "critère de Hautus" qui caractérise l’observabilité d’un groupe unitaire sur un espace de Hilbert. Il s’avère que l’analyse de Fourier utilisée ne sert qu’à "engendrer des carrés" dans un sens que l’on précisera ; vu que cela peut se faire également avec des sommes aléatoires (par exemple Gaussiennes ou Rademacher), la porte s’ouvre à une généralisation Banachique qui nous donne une caractérisation complète de l’observabilité pour des groupes bornées (discrets et continues).

• ### Lundi 29 novembre 16:00-17:00 - Yemon Choi - Lancaster University

Operator space tensor products, and cocycles on Fourier algebras

Résumé : When studying Fourier algebras of locally compact groups, it is commonly accepted that we need to use the projective tensor product of operator spaces. On the other hand, the study of derivations on Fourier algebras has revealed a potentially rich area for investigation, but such derivations can never be completely bounded,
and hence there would seem to be no reason why they should interact well with operator space tensor products.
In this talk I will explain more about these two themes, and why they presented an obstacle until recently when trying to construct non-trivial 2-cocycles on Fourier algebras. I will then outline how the obstacle can be overcome by making use of extra structure for certain derivations, together with a "twisted inclusion" result for operator space tensor products.

Lieu : 316Bbis

• ### Lundi 29 novembre 16:00-17:00 - Yemon Choi - Lancaster University

Operator space tensor products, and cocycles on Fourier algebras

Résumé : When studying Fourier algebras of locally compact groups, it is commonly accepted that we need to use the projective tensor product of operator spaces. On the other hand, the study of derivations on Fourier algebras has revealed a potentially rich area for investigation, but such derivations can never be completely bounded,
and hence there would seem to be no reason why they should interact well with operator space tensor products.
In this talk I will explain more about these two themes, and why they presented an obstacle until recently when trying to construct non-trivial 2-cocycles on Fourier algebras. I will then outline how the obstacle can be overcome by making use of extra structure for certain derivations, together with a "twisted inclusion" result for operator space tensor products.

Lieu : 316Bbis

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• ### Mardi 5 novembre 2019 13:30-15:00 - Alexandre Nou

Théorème de Marcinkiewicz (Groupe de travail)

• ### Lundi 27 novembre 2017 09:00-17:00 - Journée thematique de NC-Geom-FA

Analyse fonctionnelle et information quantique

Résumé : Benoit Collins (Universite de Kyoto)
Guillaume Aubrun (Universite de Lyon)
Participants du projet I-QUINS

• ### Du 26 mars 2018 14:00 au 27 mars 2018 17:30 - Journées en Analyse Fonctionnelle

Journées en Analyse Fonctionnelle

• ### Du 29 mai 2018 13:30 au 1er juin 2018 12:30 - Guillaume Aubrun (Lyon), Marek Cúth (Prague) et Sophie Grivaux (Lille)

Ecole de printemps 2018 du GdR AFHP

Résumé : Voir le programme ici.

• ### Mercredi 19 décembre 2018 09:00-17:30 -

Journée de jeunes analystes non commutatifs

Résumé :

• Guixiang Hong (Wuhan University) :
Vector-valued Littlewood-Paley theorem for sum and difference sets
On some properties of the differential transforms related to the fractional parabolic Poisson
semigroups
• Haonan Zhang (UFC) :
Carlen-Frank-Lieb conjecture and monotonicity of α-z Renyi relative entropy
• Simeng Wang (Université Paris Sud) :
Factoriality and type classification for q-deformed Araki-Woods algebras
• Sheng Yin (Universitat des Saarlandes) :
Free analysis : zero divisors and Atiyah properties
• Isabelle Baraquin (UFC) :
Random walks on finite quantum groups
• Xumin Wang (UFC) :
Fourier multipliers on some discrete groups

Lieu : 316Bbis

• ### Du 27 mai 2019 13:30 au 28 mai 2019 16:30 - Journées Besançon-Neuchâtel

Journées Besançon-Neuchâtel