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9 mai 2023: 1 événement

  • Séminaire d’Analyse Fonctionnelle

    Mardi 9 mai 13:45-15:00 - Charles Duquet - LMB

    Dilation Properties of measurable Schur multipliers

    Résumé : Let $N$ be a von Neumann algebra equipped with
    a normal semi-finite faithful trace (nsf trace in short) and let $T\colon N
    \to N$ be a contraction. We say that $T$ is absolutely dilatable
    if there exist another von Neumann algebra $N’$
    equipped with a nsf trace, a $w^*$-continuous trace preserving unital
    $*$-homomorphim $J\colon N\to N’$ and a trace preserving $*$-automomorphim $U\colon N’\to N’$ such that $T^k=\E U^k J$ for all integer $k\geq 0$, where $\E\colon N’\to N$ is the conditional expectation associated with $J$.
    Given a $\sigma$-finite measure space $(\Sigma,\mu)$,
    we will look at self-adjoint, unital, positive measurable bounded Schur multiplier on $B(L^2(\Sigma))$ and we will prove that there are absolutely dilatable. After that, we will remove the self-adjoint property and see what is happen. Then we characterize bounded Schur multipliers $\varphi\in L^\infty(\Sigma^2)$
    such that the Schur multiplication operator $M_\varphi\colon B(L^2(\Sigma))\to B(L^2(\Sigma))$ is absolutely dilatable.

    Lieu : Salle 324-2 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

    En savoir plus : Séminaire d’Analyse Fonctionnelle

9 mai 2023: 1 événement