A Banach space without a basis which has the bounded approximation property

DOI10.1007/BF02392555zbMath0637.46013OpenAlexW1964266328MaRDI QIDQ1099035

Stanislaw J. Szarek

Publication date: 1987

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392555

zbMATH Keywords

cotypecomplex structuresuperreflexiveunconditional finite-dimensional decompositionA Banach space without a basis which has the bounded approximation propertycartesian squareconstructing separable Banach spaces without a basislocal basis structure

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items

On conditional compactly uniform \(p\)th-order integrability of random elements in Banach spaces, A superreflexive Banach space with a finite dimensional decomposition so that no large subspace has a basis, A history of solving some famous problems in mathematical analysis, Isometric embedding of Banach spaces under optimal projection constants, Convergence of randomly weighted sums of Banach-space-valued random elements under some conditions of uniform integrability, Lipschitz-free spaces and approximating sequences of projections, An exotic quasidiagonal operator, The finite-dimensional decomposition property in non-Archimedean Banach spaces, An example of an asymptotically Hilbertian space which fails the approximation property, Covering a compact set in a Banach space by an operator range of a Banach space with basis, Quojections and finite-dimensional decompositions, A solution of the finite-dimensional homogeneous Banach space problem, On the Effective Existence of Schauder Bases, Subspaces and quotients of Banach spaces with shrinking unconditional bases, Approximation properties in fuzzy normed spaces, On Banach spaces with unconditional bases, Constructing unconditional finite dimensional decompositions, A superreflexive Banach space X with L(X) admitting a homomorphism onto the Banach algebra C(\(\beta\) N), Three space properties and basis extensions, Note on bases in algebras of analytic functions on Banach spaces, Approximation property and nuclearity on mixed‐normL^p, modulation and Wiener amalgam spaces, On Banach spaces with the commuting bounded approximation property, Compact retractions and Schauder decompositions in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The finite dimensional basis problem with an appendix on nets of Grassmann manifolds
• Counterexamples to a conjecture of Grothendieck
• Large subspaces of \(\ell^n_\infty\) and estimates of the Gordon-Lewis constant
• Diameter of the Minkowski compactum is approximately equal to n
• Subspaces without the approximation property
• The \(L_ p\) spaces
• On bases, finite dimensional decompositions and weaker structures in Banach spaces
• Factoring compact operators
• A counterexample to the approximation problem in Banach spaces
• On the Existence and Uniqueness of Complex Structure and Spaces With "Few" Operators
• Real Isomorphic Complex Banach Spaces Need not be Complex Isomorphic
• A Superreflexive Banach Space Which Does Not Admit Complex Structure
• Un théorème sur les opérateurs linéaires entre espaces de Banach qui se factorisent par un espace de Hilbert
• All separable Banach space admit for every ε>0 fundamental total and bounded by 1 + ε biorthogonal sequences
• Finite dimensional subspaces of $L_{p}$
• The Approximation Property Does Not Imply the Bounded Approximation Property
• Absolutely summing operators in $ℒ_{p}$-spaces and their applications
• Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basic
• Produits tensoriels topologiques et espaces nucléaires