Three classical problems in mathematical analysis

Abstract

The title of this dissertation alludes to the study of three classical problems of mathematical analysis. All the results that have been obtained as the fruit of four years of hard work are related, wholly or partially to at least one of the following three fields: • Banach spaces of polynomials: This is a vast field as the educated reader knows well. In particular we have studied continuity properties of polynomials on Banach spaces and topological relationships among polynomial spaces. • Algebraic genericity and lineability: This is the study of the algebraic structure within certain sets in a linear space. We give an answer to a question posed by Gurariy in the early 2000’s and, as a matter of fact, we prove a generalizationto the question formulated by Gurariy. We also link the notion of algebraic genericity to the study of sequences of operators related to Taylor series. • The classical Bohr radius problem: We provide an estimated on the n-dimensional Bohr radius for the polydisk Dn that improves other previous estimates...