Open problems in Banach spaces and measure theory

2016/07/26 by Jose Rodriguez, Rodriguez, Jose
Mathematics · #46B26 #46B50 #46E30 #46E40 #46G10 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 28B05 #Secondary: 28B20 #math.FA #msc:28B05 #msc:28B20 #msc:46B26 #msc:46B50 #msc:46E30 #msc:46E40 #msc:46G10

paper · pdf · doi:10.48550/arxiv.1607.07787

arxiv created 2016/07/26 · arxiv updated 2016/07/27

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 L^p 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 L¹ spaces) and Lebesgue-Bochner spaces (topological and structural properties, scalar convergence).

Related

• Measures and all that --- A Tutorial
• Support of Borelian Measures in Separable Banach Spaces
• L¹-spaces of vector measures with vector density
• Banach limits -- Some new thoughts and perspectives
• Compactness in the Lebesgue-Bochner spaces L^p(μ;X)