Inner and outer inequalities with applications to approximation properties

DOI10.1090/S0002-9947-2011-05241-4zbMath1241.46012OpenAlexW2039069111MaRDI QIDQ3102725

Eh. F. Oya

Publication date: 7 December 2011

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-2011-05241-4

zbMATH Keywords

Banach spacesapproximation propertiestensor normsoperator idealsspaces of operatorsfinite-rank operators

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Spaces of operators; tensor products; approximation properties (46B28) Linear spaces of operators (47L05) Operator ideals (47L20)

Related Items (13)

Operator-valued operators that are associated to vector-valued operators ⋮ On a separable weak version of the bounded approximation property ⋮ Absolutely summing operators on \(C[0,1\) as a tree space and the bounded approximation property] ⋮ The Banach ideal of \(\mathcal A\)-compact operators and related approximation properties ⋮ Principle of local reflexivity respecting subspaces ⋮ A remark on the approximation of \(p\)-compact operators by finite-rank operators ⋮ On \(\alpha\)-nuclear operators with applications to vector-valued function spaces ⋮ The convex approximation property of Banach spaces ⋮ Grothendieck's nuclear operator theorem revisited with an application to \(p\)-null sequences ⋮ A remark on Defant-Floret-Lima-Oja's conjecture ⋮ Bounded approximation properties via integral and nuclear operators ⋮ On lifting the approximation property from a Banach space to its dual ⋮ Weaker relatives of the bounded approximation property for a Banach operator ideal

Cites Work

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• Counterexamples to a conjecture of Grothendieck
• Duality in spaces of operators and smooth norms on Banach spaces
• Some geometrical properties of Banach spaces of polynomials
• Factoring weakly compact operators
• The approximation property in terms of the approximability of weak\(^*\)-weak continuous operators.
• Isometric factorization of weakly compact operators and the approximation property
• Ideals of operators, approximability in the strong operator topology, and the approximation property
• The weak metric approximation property and ideals of operators
• The strong approximation property
• Selections linéaires associees au théorème de Hahn-Banach
• Hypothèse d'approximation à l'ordre \(p\) dans les espaces de Banach et approximation d'applications \(p\) absolument sommantes
• The weak metric approximation property
• Approximation properties of orderp and the existence of non-p-nuclear operators withp-nuclear second adjoints
• Bounded approximation properties via integral and nuclear operators
• Principle of local reflexivity revisited
• Locally Complemented Subspaces and ℒp-Spaces for 0 < p < 1
• On the Approximation Properties for the SpaceH∞
• Hahn-Banach extension operators and spaces of operators
• Ideals of compact operators
• OPERATORS THAT ARE NUCLEAR WHENEVER THEY ARE NUCLEAR FOR A LARGER RANGE SPACE
• Metric approximation properties and trace mappings
• Lifting of the approximation property from Banach spaces to their dual spaces
• Extension of compact operators
• On some properties of p-nuclear and p-integral operators
• p-nukleare und p-integrale Abbildungen in Banachräumen
• Produits tensoriels d'espaces de Banach et classes d'applications linéaires
• Produits tensoriels topologiques et espaces nucléaires
• Spaces of compact operators and their dual spaces

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