AN OPERATOR SUMMABILITY OF SEQUENCES IN BANACH SPACES

DOI10.1017/S0017089513000360zbMath1301.46004arXiv1207.3620MaRDI QIDQ5415964

Anil Kumar Karn, Deba Prasad Sinha

Publication date: 19 May 2014

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.3620

zbMATH Keywords

Dunford-Pettis propertyabsolutely summing operatorsGelfand-Phillips propertylimited setsweakly \(p\)-summablenorm summable sequencesoperator \(p\)-summable

Mathematics Subject Classification ID

Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Compactness in Banach (or normed) spaces (46B50)

Related Items (11)

Duality of measures of non-${\mathcal A}$-compactness ⋮ A class of sets in a Banach space coarser than limited sets ⋮ Summability of sequences and extensions of operator ideals ⋮ Ideals of mid \(p\)-summing operators: a tensor product approach ⋮ A note on \(p\)-limited sets in dual Banach spaces ⋮ Isomorphic properties in spaces of compact operators ⋮ Some properties of 𝑝-limited sets ⋮ An anisotropic approach to mid summable sequences ⋮ Sequentially Right Banach spaces of order $p$ ⋮ Unnamed Item ⋮ CLASSES OF SEQUENTIALLY LIMITED OPERATORS

Cites Work

• The \(p\)-approximation property in terms of density of finite rank operators
• Weakly \(p\)-compact, \(p\)-Banach-Saks, and super-reflexive Banach spaces
• On subspaces of L\(^p\)
• Compact operators whose adjoints factor through subspaces of l_p
• $p$-Convergent sequences and Banach spaces in which $p$-compact sets are $q$-compact
• Weak Compactness and Vector Measures
• Operators whose adjoints are quasi p-nuclear
• Limited Operators and Strict Cosingularity
• Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du Type C(K)

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