Banach Spaces With Separable Duals

DOI10.2307/2001128zbMath0706.46015OpenAlexW4256157456MaRDI QIDQ3487994

M. Zippin

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2001128

zbMATH Keywords

every Banach space with a separable dual embeds into a space with a shrinking basisevery separable reflexive space can be embedded in a reflexive space with a basis

Mathematics Subject Classification ID

Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items (21)

On Zippin's embedding theorem of Banach spaces into Banach spaces with bases ⋮ Genericity and amalgamation of classes of Banach spaces ⋮ Isometric embedding of Banach spaces under optimal projection constants ⋮ The convex point of continuity property in Banach spaces not containing \(\ell _{1}\) ⋮ The universality of \(\ell _{1}\) as a dual space ⋮ The cofinal property of the reflexive indecomposable Banach spaces ⋮ Small subspaces of \(L_p\) ⋮ Banach Space-valued Extensions of Linear Operators on L∞ ⋮ A characterization of subspaces and quotients of reflexive Banach spaces with unconditional bases ⋮ Uniformly factoring weakly compact operators ⋮ The point of continuity property in Banach spaces not containing \(\ell_1\) ⋮ The uniform structure of Banach spaces ⋮ On various modes of scalar convergence in \(L_0({\mathfrak X})\) ⋮ A universal reflexive space for the class of uniformly convex Banach spaces ⋮ Duality on Banach spaces and a Borel parametrized version of Zippin's theorem ⋮ Geometry of Banach spaces having shrinking approximations of the identity ⋮ Non-universal families of separable Banach spaces ⋮ Zippin’s embedding theorem and amalgamations of classes of Banach spaces ⋮ The convex point of continuity property in Asplund spaces ⋮ Upper and lower estimates for Schauder frames and atomic decompositions ⋮ Trees and branches in Banach spaces

Cites Work

• Factoring weakly compact operators
• The separable extension problem
• Some problems on bases in Banach and Frechet spaces
• On bases, finite dimensional decompositions and weaker structures in Banach spaces
• Classical Banach spaces
• AN EXTREME POINT CRITERION FOR SEPARABILITY OF A DUAL BANACH SPACE, AND A NEW PROOF OF A THEOREM OF CORSON
• On ω*-basic sequences and their applications to the study of Banach spaces
• On shrinking basic sequences in Banach spaces
• Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basic

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