Tightness in Banach spaces

Author(s)

Alejandra Carolina Caceres Rigo

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2022-02-24

Examining board members

Valentin Raphael Henri Ferenczi; Jorge Lopez Abad; Leandro Fiorini Aurichi; Christina Brech; Samuel Gomes da Silva

• Advisor: Valentin Raphael Henri Ferenczi

Abstract

In this work, we study Banach spaces with tight bases and we prove dichotomies involving different types of minimality and new types of tightness. We introduce the notion of admissible system of blocks to code various kinds of embeddings between Banach spaces with Schauder bases. We extend the definition of tight Schauder basis and tight-with-constants Schauder basis to the case of Banach spaces with transfinite basis. We give characterizations of these notions in this context and study their properties. (AU)

• FAPESP's process: 17/18976-5 - Study of the borelian complexity of certain properties of Banach spaces
• Grantee: Alejandra Carolina Cáceres Rigo
• Support Opportunities: Scholarships in Brazil - Doctorate