Open problems in Banach spaces and measure theory

  • José Rodríguez
Keywords: Banach space, Baire σ-algebra, Borel σ-algebra, measurable selector, Riemann integral, Pettis integral, McShane integral, vector measure, Lebesgue-Bochner space

Abstract

We collect several open questions in Banach spaces, mostly related to measure theoretic aspects of the theory. The problems are divided into five categories: miscellaneous problems in Banach spaces (non-separable Lp spaces, compactness in Banach spaces, w*-null sequences in dual spaces), measurability in Banach spaces (Baire and Borel σ-algebras, measurable selectors), vector integration (Riemann, Pettis and McShane integrals), vector measures (range and associated L1spaces) and Lebesgue-Bochner spaces (topological and structural properties, scalar convergence).

Keywords: Banach space, Baire σ-algebra, Borel σ-algebra, measurable selector, Riemann integral, Pettis integral, McShane integral, vector measure, Lebesgue-Bochner space

Published
2017-10-03
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606