$p$-Convergent sequences and Banach spaces in which $p$-compact sets are $q$-compact

DOI10.1090/S0002-9939-2010-10508-7zbMath1270.47018MaRDI QIDQ3085059

J. M. Delgado, Cándido Piñeiro

Publication date: 28 March 2011

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

zbMATH Keywords

absolutely \(p\)-summing operators\(p\)-null sequencesrelatively \(p\)-compact setsvector measures of bounded variation

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Linear operators defined by compactness properties (47B07) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Compactness in Banach (or normed) spaces (46B50)

Related Items (16)

On ‐null sequences and their relatives ⋮ Unconditionally p-null sequences and unconditionally p-compact operators ⋮ Spaceability of sets of \(p\)-compact maps ⋮ On approximation properties related to unconditionally p‐compact operators and Sinha–Karn p‐compact operators ⋮ Compactness principles for topological vector spaces ⋮ 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 ⋮ The ideal of $p$-compact operators and its maximal hull ⋮ On \(\alpha\)-nuclear operators with applications to vector-valued function spaces ⋮ Polynomials and holomorphic functions on \(\mathcal{A}\)-compact sets in Banach spaces ⋮ AN OPERATOR SUMMABILITY OF SEQUENCES IN BANACH SPACES ⋮ Grothendieck's nuclear operator theorem revisited with an application to \(p\)-null sequences ⋮ Compactness in the space of $p$-continuous vector-valued functions ⋮ The \(E\)-compactness and the \(E\)-approximation property determined by the Banach space \((\sum \ell_p)_q\) ⋮ Sequentially right-like properties on Banach spaces ⋮ On some measures of non-compactness associated to Banach operator ideals

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