The Banach Space c0
The Banach Space c0
The paper is a survey on recent progress on properties of the Banach space \(c_0\). A sequence space characterization is given for a Banach space to be isometric to a subspace of \(c_0\) and its consequences is investigated. It is shown that \(c_0\) is minimal among sufficiently smooth non-reflexive spaces and maximal among asymptotically flat spaces. The paper also studies approximation properties for subspaces of \(c_0\). Some open problems are collected in the end of the survey.
Subspaces, 12 Matemáticas, 1202.03 Álgebra y Espacios de Banach, 1202 Análisis y Análisis Funcional, asymptotically flat spaces, Subespacios, Polyhedral, smooth non-reflexive spaces, 530, Espacios de Banach, 510, Banach spaces, Geometry and structure of normed linear spaces, approximation properties, Poliédrico, Classical Banach spaces in the general theory, Spaces of operators; tensor products; approximation properties
Subspaces, 12 Matemáticas, 1202.03 Álgebra y Espacios de Banach, 1202 Análisis y Análisis Funcional, asymptotically flat spaces, Subespacios, Polyhedral, smooth non-reflexive spaces, 530, Espacios de Banach, 510, Banach spaces, Geometry and structure of normed linear spaces, approximation properties, Poliédrico, Classical Banach spaces in the general theory, Spaces of operators; tensor products; approximation properties
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