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7 juin 2022: 1 événement

  • Séminaire d’Analyse Fonctionnelle

    Mardi 7 juin 13:45-14:45 - Yoël Perreau - LmB

    Asymptotic geometry and Delta-points

    Résumé : Daugavet- and Delta-points are natural localizations of geometric characterizations of the Daugavet property and of spaces with bad projections (also known as spaces with the diametral local diameter two property). An element $x$ in the unit sphere of a Banach space $X$ is called a Daugavet-point if every slice of the unit ball of $X$ contains elements which can be taken at distance arbitrarily close to 2 from the point $x$, and it is called a Delta-point if it only satisfies this requirement for slices containing $x$. Since their introduction those points have been systematically studied in classical Banach spaces, and surprising nonintuitive examples of Banach spaces with strong seemingly opposite isomorphic properties in which Daugavet-points exist have been discovered. In this talk we look for isometric properties providing an obstruction to the existence of Daugavet- and Delta-points in a given Banach space. In particular we study the influence of the asymptotic geometry of a Banach space on the existence of those points and we provide new examples of Banach spaces which fail to contain them.

    En savoir plus : Séminaire d’Analyse Fonctionnelle