AD points and the super ADP property for Banach spaces

Inicio: 12 marzo 2025 09:00
Final: 12 marzo 2025 10:00
Categorías: Conference , Seminar , Instituto de Matemáticas UGR

Where: Seminario Departamento Análisis Matemático, Facultad de Ciencias

IMAG Functional Analysis Seminar
Title: AD points and the super ADP property for Banach spaces
By Marcus Loo (University of Tartu, Estonia)
Abstract: The Daugavet property offers a nice geometric characterization in terms of slices of the unit ball. This provided a natural way to consider a localization of the Daugavet property, called a Daugavet point. Stronger versions of the Daugavet points were introduced by M. Mart\'in, Y. Perreau and A. Rueda Zoca, called the super Daugavet and ccs Daugavet points. In 2004, M. Mart\'in and T. Oihkberg introduced the Alternative Daugavet property (ADP), connected to the Daugavet property. In this talk, we consider natural localizations of ADP, called AD points and super AD points. We aim to distinguish between all the notions, by looking at examples. Secondly, we consider the super ADP property for Banach spaces, induced by super AD points. It is known that the different variants of Daugavet points all induce the (same) global Daugavet property. This is not the case for the point-wise versions of the ADP. In the talk, we will provide examples of spaces with the super ADP and prove that they cannot have the CPCP (hence, they also fail PCP and RNP).