An example of an asymptotically Hilbertian space which fails the approximation property

DOI10.1090/S0002-9939-01-06142-1zbMath0983.46022arXivmath/0006134MaRDI QIDQ2723500

César L. García, Peter G. Casazza, William B. Johnson

Publication date: 5 July 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0006134

zbMATH Keywords

unconditional basisapproximation propertyweak Hilbert spaceasymptotically Hilbertian property

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Local theory of Banach spaces (46B07) Spaces of operators; tensor products; approximation properties (46B28) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items (10)

Hereditary approximation property ⋮ Lipschitz-free spaces and approximating sequences of projections ⋮ On $$ \mathbb Z_d $$ -symmetry of spectra of some nuclear operators ⋮ Subspaces of \(\ell_2 (X)\) without the approximation property ⋮ The trace formula in Banach spaces ⋮ The ergodicity of weak Hilbert spaces ⋮ On uniformly finitely extensible Banach spaces ⋮ Some approximation properties and nuclear operators in spaces of analytical functions ⋮ Non-ergodic Banach spaces are near Hilbert ⋮ On linear operators with \(s\)-nuclear adjoints, \(0<s\leq 1\)

Cites Work

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• On Tsirelson's space
• A Banach space without a basis which has the bounded approximation property
• Banach lattices with property \(( H )\) and weak Hilbert spaces
• The dimension of almost spherical sections of convex bodies
• Weak Hilbert Spaces
• The Approximation Problem for Banach Spaces

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