Density of finite rank operators in the Banach space of \(p\)-compact operators

DOI10.1016/j.jmaa.2010.04.058zbMath1205.46010OpenAlexW1971023967MaRDI QIDQ984807

J. Martínez

Publication date: 20 July 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.04.058

zbMATH Keywords

\(L^p\)-spacetrace functional\(p\)-summing operator\(p\)-nuclear operator\(p\)-approximation propertySaphar's approximation property\(p\)-compact operator\(p\)-integral operatorquasi \(p\)-nuclear operatorrelatively \(p\)-compact set

Mathematics Subject Classification ID

Linear operators defined by compactness properties (47B07) 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) Compactness in Banach (or normed) spaces (46B50)

Related Items (22)

On ‐null sequences and their relatives ⋮ On approximation properties related to unconditionally p‐compact operators and Sinha–Karn p‐compact operators ⋮ The ideal of weakly p-compact operators and its approximation property for Banach spaces ⋮ The Banach ideal of \(\mathcal A\)-compact operators and related approximation properties ⋮ Banach compactness and Banach nuclear operators ⋮ A remark on the approximation of \(p\)-compact operators by finite-rank operators ⋮ The injective and surjective hulls of the ideal of \((p,q)\)-compact operators and their approximation properties ⋮ On \(\alpha\)-nuclear operators with applications to vector-valued function spaces ⋮ Grothendieck's nuclear operator theorem revisited with an application to \(p\)-null sequences ⋮ A note on \(p\)-limited sets ⋮ Behavior of holomorphic mappings on $p$-compact sets in a Banach space ⋮ Uniform factorization for \(p\)-compact sets of \(p\)-compact linear operators ⋮ $p$-Convergent sequences and Banach spaces in which $p$-compact sets are $q$-compact ⋮ SOME RESULTS OF THE -APPROXIMATION PROPERTY FOR BANACH SPACES ⋮ On \(p\)-compact mappings and the \(p\)-approximation property ⋮ Compactness in the space of $p$-continuous vector-valued functions ⋮ Unnamed Item ⋮ Quotient algebras of Banach operator ideals related to non-classical approximation properties ⋮ THE -APPROXIMATION PROPERTY AND ITS DUALITY ⋮ The \(E\)-compactness and the \(E\)-approximation property determined by the Banach space \((\sum \ell_p)_q\) ⋮ On some measures of non-compactness associated to Banach operator ideals ⋮ Weaker relatives of the bounded approximation property for a Banach operator ideal

Cites Work

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• The \(p\)-approximation property in terms of density of finite rank operators
• Subspaces without the approximation property
• On linear operators with \(p\)-nuclear adjoints
• Hypothèse d'approximation à l'ordre \(p\) dans les espaces de Banach et approximation d'applications \(p\) absolument sommantes
• Compact operators whose adjoints factor through subspaces of l_p
• Approximation properties of orderp and the existence of non-p-nuclear operators withp-nuclear second adjoints
• Operators whose adjoints are quasi p-nuclear
• Compact operators which factor through subspaces of l_p
• Absolutely summing operators in $ℒ_{p}$-spaces and their applications
• 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

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