The Gelfand--Phillips property in closed subspaces of some operator spaces

By introducing the concepts of strongly limited completely continuous and strongly Dunford-Pettis completely continuous subspaces of operator ideals, it will be given some characterizations of these concepts in terms of lcc ness and DPcc ness of all their evaluation operators related to that subspace. In particular, when X * or Y has the Gelfand-Phillips (GP) property, we give a characterization of GP property of a closed subspace M of compact operators K (X , Y ) in terms of strong limited complete continuity of M. Also it is shown that, each operator ideal U(X , Y ) is strongly limited completely continuous, iff, X * and Y have the GP property. KeywordsGelfand-Phillips property • Completely continuous algebra • Strongly completely continuous algebra • Limited completely continuous operator Mathematics Subject Classification 47L05 • 47L20 • 46B28 • 46B99 B Halimeh Ardakani

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“…On the other hand, by hypothesis, for each w * ∈ W * , ψ R * w * is lcc (resp., DPcc) and from [18,22]…”

Section: Strongly Limited Completely Continuous Spacesmentioning

confidence: 99%

Strongly limited (Dunford–Pettis) completely continuous subspaces of operator ideals

2019

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“…An operator T : X → Y is called limited completely continuous (lcc) if it maps limited weakly null sequences to norm null sequences, see [22].…”

Section: A Seriesmentioning

confidence: 99%

A note on Dunford-Pettis like properties and complemented spaces of operators

Ghenciu¹

2018

Commentationes Mathematicae Universitatis Carolinae

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“…In [28] the authors, using Theorem 2, gave a sufficient condition in order that a closed subspace of the space K(X, Y ) has the Gelfand Phillips property. Using Theorem 10, we can state the following Theorem 11.…”

Section: Be a Linear Continuous Operator And Letmentioning

confidence: 99%

Some isomorphic properties in $K(X,Y)$ and in projective tensor products

Cilia

Emmanuele

2017

Colloq. Math.

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We study the (DPrcp) and the Gelfand Phillips property in the space of compact operators. Moreover we give some sufficient conditions in order that a projective tensor product of two Banach spaces is sequentially Right (SR) or it has the L-limited property. Moreover we study the Bourgain Diestel property (BD), the (RDP *) property in the space K w * (X, Y). We introduce the dual (SR *) property and we give a characterization of it.

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The Gelfand--Phillips property in closed subspaces of some operator spaces

Cited by 31 publications

References 13 publications

Strongly limited (Dunford–Pettis) completely continuous subspaces of operator ideals

Strongly limited (Dunford–Pettis) completely continuous subspaces of operator ideals

A note on Dunford-Pettis like properties and complemented spaces of operators

Some isomorphic properties in $K(X,Y)$ and in projective tensor products

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