A counterexample to the approximation problem in Banach spaces
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This article is published in Acta Mathematica.The article was published on 1973-07-01 and is currently open access. It has received 370 citations till now. The article focuses on the topics: Banach manifold & Counterexample.read more
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Operator Algebras: Theory of C*-Algebras and von Neumann Algebras
TL;DR: In this article, the authors present a model for operators on Hilbert Space, including C*-Algebras, Von Neumann Algebra, and K-Theory and Finiteness.
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The unconditional basic sequence problem
W. T. Gowers,B. Maurey +1 more
TL;DR: In this article, a Banach space that does not contain any infinite un-conditional basic sequence was constructed and further properties of this space were investigated, such as the fact that every operator on the space is a strictly singular perturbation of a multiple of the identity.
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The unconditional basic sequence problem
W. T. Gowers,B. Maurey +1 more
TL;DR: In this paper, a Banach space that does not contain any infinite unconditional basic sequence is constructed, and it is shown that this space does not have any infinite basic sequence in it.
BookDOI
A basis theory primer
TL;DR: In this paper, the Fourier Transform on the Real Line is used to transform the real line into a Fourier series, and Wavelet Bases and Frames are used in applied harmonic analysis.
Journal ArticleDOI
Compact holomorphic mappings on Banach spaces and the approximation property
TL;DR: In this article, the authors studied the approximation properties of complex valued holomorphic functions on a complex Banach space and showed that the compact-open topology has the approximation property if and only if E has the approximate property.
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Produits Tensoriels Topologiques Et Espaces Nucleaires
TL;DR: In this paper, Bourbaki implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
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On bases, finite dimensional decompositions and weaker structures in Banach spaces
William B. Johnson,William B. Johnson,Haskell P. Rosenthal,Haskell P. Rosenthal,M. Zippin,M. Zippin +5 more
TL;DR: In this article, the connections between bases and weaker structures in Banach spaces and their duals are investigated, and it is shown that every separable π-structures and finite dimensional Schauder decomposition has a basis.
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A complementary universal conjugate Banach space and its relation to the approximation problem
TL;DR: In this paper, it was shown that every Banach space has the metric approximation property (m] a.a.p., in short) iff (ΣG�Ω(G� *� )� (G� *)ⓘ m� Ω mⓘ does not, and if there is a space failing the m. a.p, then the space can be equivalently normed to fail m. p.