Classification of Banach Spaces --its Topological and Cardinality Properties

2002/11/19 by Eugene Tokarev, Tokarev, Eugene
Mathematics · #46B20 (Primary) 46B07 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B07 #msc:46B20

paper · pdf · doi:10.48550/arxiv.math/0211298

Latex2e

arxiv created 2002/11/19 · arxiv updated 2009/11/30

Abstract

Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected topological spaces. Results are used in the problem of synthesis of Banach spaces, and to describe omittable spaces that are defined below.

Related

• Genus n Banach spaces
• Banach spaces without minimal subspaces - examples
• The Uniform Classification of Banach Spaces
• Incomparable, non isomorphic and minimal Banach spaces
• A continuum of totally incomparable hereditarily indecomposable Banach spaces