## 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).

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 la responsable (Yulia Kuznetsova) : yulia.kuznetsova@univ-fcomte.fr.
Pour s’abonner au séminaire : ACM.

### Décembre

-Mardi 4 décembre : Christian Le Merdy, UFC
Différentiabilité à l’ordre n pour les fonctions d’opérateurs dans les classes de Schatten

-Mardi 11 décembre : Pavel Zorin-Kranich, University of Bonn
Decoupling for moment manifolds

-Mercredi 19 décembre : Journée de jeunes analystes non commutatifs
Programme + résumés

### Novembre

-Mardi 6 novembre : relâche

-Mardi 13 novembre : Thomas Scheckter, UNSW Sydney
A Noncommutative Generalisation of a Problem of Steinhaus

-Mardi 20 novembre : Waed Dada, Université Wuppertal
Cesàro bounded operators on Banach spaces

-Mardi 27 novembre : Romuald Ernst, Université du Littoral Côte d'Opale
Quelques remarques autour de la fréquente hypercyclicité commune

### Octobre

-Mardi 2 octobre : Gilles Lancien, UFC
(Exceptionnellement dans la salle 324B-2)
Espaces de Banach réflexifs asymptotiquement $c_0$ et plongements grossiers

-Mardi 9 octobre : relâche (journées GdR AFHP, Nice)

-Mardi 16 octobre : Matěj Novotný, Czech technical university
Schauder Bases in Lipschitz Free Spaces

-Mardi 23 octobre : Ali Talebi, Ferdowsi University of Mashhad, Iran
Noncommutative tail probability of maximal sums

### Septembre

-Mardi 11 septembre: B.V.R. Bhat, .
Infinite mode quantum Gaussian states

-Mardi 18 septembre: Jared White, .
Finitely generated ideals in group algebras

-Mardi 25 septembre: Haonan Zhang, .
Idempotent states on quantum groups

## Agenda

• ### Mardi 12 décembre 2017 13:45-15:00 - Monika Malczak - Greifswald

Lévy processes on braided *-bialgebras

Résumé : In order to use Majid’s Bosonization/Symmetrization of braided bialgebras for quantum
probability theory, we give an extension to braided *-bialgebras, which is based on a
joint work by Franz, Schott and Schürmann [1]. Furthermore we investigate a connection between quantum Lévy processes on braided *-bialgebras and their symmetrization. We present a realization as solution of quantum stochastic differential equations for Brownian motions on such braided structures, which can be considered as multi-dimensonal analogues of the Azéma martingales.
References
[1] Franz, Uwe ; Schott, René ; Schürmann, Michael : Lévy Processes and Brownian Motion on Braided Spaces. In : Franz, Uwe : The Theory of Quantum Lévy Processes, Chapter 5 of habilitation thesis.
2003. Available at https://arxiv.org/abs/math/0407488.

• ### Mardi 12 décembre 2017 15:00-16:00 - Philipp Varso - Greifswald

Central Limit Theorem for General Universal Products

Résumé : To model independence in quantum probability theory one uses so-called universal products, which are in general described by tensor categories of algebraic quantum probability spaces $(A,\varphi)$. In [1] Muraki has shown how to classify such products and in particular obtained that only -five universal products exist. But there are examples which do not -fit into Muraki’s framework, for instance if one wants to deal with a tuple of linear functionals $\varphi^(i)$ on the algebra $A$ like it has been done in the case of $c$-freeness by Bo\.zejko and Speicher in [2].
The case of bi-freeness by Voiculescu [3], where in particular the underlying algebra $A$ is isomorphic to the free product of two algebras $A^(1)$ and $A^(2)$, is also not covered by Muraki’s classi-cation. In [4] Schürmann and Manzel present a uni-fied approach to cumulants, which includes the above concepts of independence. This is achieved by considering a certain category of algebraic non-commutative probability spaces, denoted by $\rm algP_d,m$, which consist of an $m$-tuple of subalgebras and a $d$-tuple of linear functionals and therefore allows to investigate $(d,m)$-independence induced by a so-called u.a.u.-product.
The -first noncommutative version of a central limit theorem dates back to von Waldenfels [5]. In this talk we want to present a noncommutative version of a central limit theorem for a u.a.u.-product in $\rm algP_d,m$, where we make use of the so-called Lachs functor [6], which operates between certain tensor categories.
References
[1] Muraki, Naofumi : The -five independences as natural products. In-n. Dimens. Anal. Quantum Probab. Relat. Top. 6.3 (2003), 337-371.
[2] Bo\.zejko, Marek ; Speicher, Roland : $\psi$ -independent and symmetrized white noises. In : Quantum probability \& related topics. QP-PQ, VI, 219-236. World Sci. Publ., River Edge, NJ, 1991.
[3] Voiculescu, Dan-Virgil : Free probability for pairs of faces I. Comm. Math. Phys. 332.3 (2014), 955-980.
[4] Manzel, Sarah ; Schürmann, Michael : Non-Commutative Stochastic Independence and Cumulants. Preprint arXiv:1601.06779 (2016), 42 pages. To appear in IDAQP 20.2 (2017).
[5] von Waldenfels, W. : An algebraic central limit theorem in the anti-commuting case. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 42.2 (1978), 135-140.
[6] Lachs, Stephanie : A New Family of Universal Products and Aspects of a Non-Positive Quantum Probability Theory. PhD thesis. Ernst-Moritz-Arndt-Universität Greifswald, 2015.

• ### Mardi 19 décembre 2017 13:45-15:00 - Ignacio Vergara - ENS Lyon

Résumé : Les multiplicateurs de Schur sont des fonctions à deux variables sur un ensemble $X$ qui définissent des opérateurs bornés sur $B(\ell_2(X))$ par multiplication des coefficients matriciels. Lorsque l’ensemble $X$ est un graphe, on peut étudier le cas particulier des multiplicateurs radiaux, c’est-à-dire, des fonctions que ne dépendent que de la distance entre chaque paire de sommets.
Les multiplicateurs radiaux sur un arbre homogène ont été caractérisés par Haagerup, Steenstrup et Szwarc en termes de certaines matrices de Hankel. Dans cet exposé, je présenterai des extensions de ce résultat à des produits d’arbres, des produits de graphes hyperboliques et aux complexes cubiques CAT(0) de dimension finie.

• ### Mardi 16 janvier 13:45-15:00 - Un Cig Ji

Inequalities for Positive Module Operators on von Neumann Algebras

Résumé : We establish the Cauchy-Schwarz and Golden-Thompson inequalities for module operators, a generalization of a (noncommutative) conditional expectation, on a von Neumann algebra. We apply these inequalities to the Bennett inequality and a uncertainty relation, a generalization of the Schrödinger uncertainty relation, for conditional expectations. This is a joint work with B. J. Choi and Y. Lim.

Lieu : salle 324B2

• ### Mardi 6 février 13:45-15:00 - Safoura Zadeh - IMPAN (Varsovie)

Markov’s problem for k-absolutely monotone polynomials

Résumé : Studying the specific gravity of a solution as a function of the percentage of the dissolved substance D. Mendeleev came across a problem that, in mathematical term, asks how large $|p’(x)|$ on $[-1,1]$ can be if $p(x)$ is a quadratic polynomial with $|p(x)|\leq 1$ on $[-1,1]$. Mendeleev showed that $|p’(x)|\leq 4$ and talked to A. A. Markov about the problem. Markov found the question fascinating and studied the problem for a real polynomial of degree at most n. He proved that $|p’(x)| \leq n^2$ on $[-1,1]$ when $|p(x)|\leq 1$ on $[-1,1]$. Later Markov’s brother V. A. Markov studied the problem for the $m$-th derivative, when $m<n$.
In this talk we study Markov’s problem for $m$-th derivative of a family of polynomials called k-absolutely monotone polynomials. As a consequence, we obtain a sharp version of Bernstein inequality for monotone polynomials as well as a new simple proof of Markov’s inequality for monotone polynomials. This is based on a joint work with Oleksiy Klurman.

• ### Mardi 13 février 13:45-15:00 - Kangwei Li - Basque Center for Applied Mathematics (Bilbao)

Extrapolation for multilinear Muckenhoupt class of weights and applications

Résumé : In this talk, I will introduce our recent progress on extrapolation theory. In the linear case, the extrapolation theory is well understood. However, in the multilinear case, the extrapolation was only known for product $A_p$ weights. The multilinear $A_\vec P$ weight, which was introduced in 2009, no extrapolation theory was known before. In this talk, I will give a full solution to this problem. As applications, we can improve the weighted estimates for the bilinear Hilbert transform, the multilinear Marcinkiewicz-Zygmund inequality etc. This talk is based on joint work with José María Martell and Sheldy Ombrosi.

• ### Mardi 27 février 13:45-15:00 - Gaspar Mora - Universidad de Alicante

On the distribution of the zeros of exponential polynomials

Résumé : In this talk we analyse the distribution of the zeros of exponential
polynomials
$h(z) :=1+\sum_k=1^N a_k e^-zr_k$ ; $z, a_k\in \mathbb C$, $r_k>0$, $N\geq 1$
by means of the structure of the set $R_h(z) :=\overline\ \Re z:h(z)=0\$.
Our special interest is focused when $h(z)$ is a
partial sum of the Riemann zeta function or a partial sum of the Dirichlet
alternating series.

• ### Lundi 5 mars 13:30-15:00 - Oleg Aristov - Moscou

Séminaire d’Analyse Fonctionnelle

• ### Mardi 13 mars 13:45-15:00 - Anna Skripka - University of New Mexico

Schur multipliers in perturbation theory

Résumé : We will recall classical Schur multipliers acting on matrices and
consider their generalizations to multilinear transformations arising in
infinite dimensional perturbation theory. As an application, we will
discuss several recent results on approximation of operator functions.

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

Journées en Analyse Fonctionnelle

• ### Du 29 mai 13:30 au 1er juin 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 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
• Chao Zhang (Universidad Autonoma de Madrid) 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