## Les événements de mars 2023

• ### Jeudi 16 mars 14:00-15:30 - Damien Galant - Université de Mons et Université Polytechnique Hauts-de-France

Séminaires Equations aux Dérivées Partielles

Résumé : Sur la notion de "ground state" pour l’équation de Schrödinger non-linéaire sur des graphes métriques.

Lieu : 31B-31B BIS

• ### Mardi 7 mars 13:45-15:00 - Purbayan Chakraborty - LMB

Error basis and characterisation of semigroups of positive maps

Résumé : An unitary error basis on $M_n$ is a generalisation of Pauli matrices which form an orthonormal basis of $M_2$ with respect to Hilbert-Schmidt inner product. Taking advantage of the isomorphism between $M_n\otimes M_n$, $L(M_n)$ the space of linear maps from $M_n$ to itself and $M_n^2$, these unitary error bases are very useful to get a suitable discrete Fourier expansion of a map $T\in L(M_n)$ . These discrete Fourier coefficients which can be thought of as an $n^2\times n^2$ matrix, give many information about different positivity property of the map $T$.
We will discuss a generalised version of Schoenberg correspondence for positive semigroup leading to the characterisation of k-(super)positive operators. As an explicit application we will apply our result for the characterisation of all positive semigroup of linear maps on $M_2$ using Pauli basis.

Lieu : Salle 316 B bis (3ème étage) - Laboratoire de Mathématiques de Besançon (LmB)
Campus de la Bouloie, bâtiment Métrologie B
Université de Franche-Comté
16 route de Gray
25030 Besançon

• ### Lundi 13 mars 12:05-13:05 - Colin Petitjean - Univrsité Gustav Eiffel

Around composition operators between spaces of Lipschitz functions

Résumé : If $f : M \to N$ is any map between metric spaces, then the composition (by $f$) operator is defined by $g \in \mathrmLip(N) \mapsto g \circ f \mathrmLip(M)$. Here $\mathrmLip(M)$ stands for a Banach space of scalar-valued Lipschitz maps defined on M. In this talk, we will focus on some classical operator properties such as : boundedness, injectivity, surjectivity, (weak) compactness, etc. We will approach the questions from a different perspective than most articles in the literature. Indeed, we will move our focus to a lower stage by studying the pre-adjoint operator. Finally, we will study the weighted versions of these composition operators with a similar approach.

• ### Mardi 14 mars 13:45-14:45 - Triinu Veeorg - Université de Tartu

Daugavet and Delta points in Banach spaces

Résumé : A norm one element $x$ of a Banach space is a Daugavet point (respectively, a $\Delta$-point) if every slice of the unit ball (respectively, every slice of the unit ball containing $x$) contains an element that is almost at distance 2 from $x$.
We start the talk by characterizing Daugavet points in Lipschitz-free spaces. We apply the characterization to provide an example of a Lipschitz-free space with the Radon-Nikodym property and a Daugavet point, which is the first example of such a Banach space. We also consider renormings of some Banach spaces, including $\ell_2$, that provide $\Delta$-points or Daugavet points.

• ### Mardi 21 mars 13:45-14:45 - Colin Petitjean - Univrsité Gustav Eiffel

Around composition operators between spaces of Lipschitz functions

Résumé : If $f : M \to N$ is any map between metric spaces, then the composition (by $f$) operator is defined by $g \in Lip(N) \mapsto g \circ f \in Lip(M)$. Here $Lip(M)$ stands for a Banach space of scalar-valued Lipschitz maps defined on M. In this talk, we will focus on some classical operator properties such as : boundedness, injectivity, surjectivity, (weak) compactness, etc. We will approach the questions from a different perspective than most articles in the literature. Indeed, we will move our focus to a lower stage by studying the pre-adjoint operator. Finally, we will study the weighted versions of these composition operators with a similar approach.

• ### Mardi 28 mars 13:45-15:00 - Reshmi MN - Indian Institute of Technology, Bombay

Characteristic functions and colligations

Résumé : We associate a certain co-isometric observable colligations with contractive lifting and show that the characteristic function of lifting is complete invariant for minimal contractive lifting. A class of co-isometric observable colligations with input spaces of finite dimension is characterized. Blaschke factor based transformations of the characteristic function of lifting are studied.

Lieu : Salle 316 B bis (3ème étage) - Laboratoire de Mathématiques de Besançon (LmB)
Campus de la Bouloie, bâtiment Métrologie B
Université de Franche-Comté
16 route de Gray
25030 Besançon