Analysis & Applications Seminar

Integration for quasi-Banach-space-valued functions

Speaker:  Glenier Bello (UAM)
Date:  Thursday, 02 June 2022 - 11:30
Place:  Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Online: (ID: 876 3760 1676)


In this talk we will present a new approach to define a suitable integral for functions with values in quasi-Banach spaces. The integrals of Bochner and Riemann have deficiencies in the non-locally convex setting. The study of an integral for p-Banach spaces initiated by Vogt is neither totally satisfactory, since there are quasi-Banach spaces which are p-convex for all 0 < p < 1, so it is not always possible to choose an optimal p to develop the integration. Our method puts the emphasis on the galb of the space, which permits a precise definition of its convexity. The integration works for all spaces of galbs known in the literature. We will finish with a fundamental theorem of calculus.

The talk will be based on a joint work with José Luis Ansorena (Universidad de La Rioja).