Duality between spaces of \(p\)-summable sequences, \((p,q)\)-summing operators and characterizations of nuclearity

DOI10.1007/BF01360858zbMath0304.47025MaRDI QIDQ1216833

Heikki Apiola

Publication date: 1976

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/182756

Mathematics Subject Classification ID

Sequence spaces (including Köthe sequence spaces) (46A45) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Tensor products in functional analysis (46M05)

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Operator-valued operators that are associated to vector-valued operators ⋮ \(\phi\)-summing operators in Banach spaces ⋮ Banach space of strongly \((p,q,\sigma)\)-summable sequences and applications ⋮ Factorization of strongly (p,σ)-continuous multilinear operators ⋮ Operator ideals generated by strongly Lorentz sequence spaces ⋮ Strongly (p,q)-summable sequences ⋮ Absolutely \((r,q)\)-summing operators on vector-valued function spaces ⋮ Duality theory for generalized summing linear operators ⋮ Coincidence Results for Summing Multilinear Mappings ⋮ Vector-valued Lorentz sequence spaces and their dual spaces ⋮ Domination and factorization theorems for positive strongly \(p\)-summing operators ⋮ Some mapping properties of \(p\)-summing adjoint operators ⋮ Die Nuklearität der Ultradistributionsräume und der Satz vom Kern. II ⋮ The Littlewood-Orlicz operator ideal ⋮ On some Banach space sequences

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