Some classes of Banach spaces and complemented subspaces of operators
type: Item
instance of: scholarly article
title: Some classes of Banach spaces and complemented subspaces of operators
zbMATH Open document ID: 1416.46024
published in: Advances in Operator Theory
publication date: 2019-01-31T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aot/1543633232
review text: Let $X$ be a Banach space. In this paper, the author continues her work (see [Acta Math. Hung. 157, No. 1, 63--79 (2019; Zbl 1438.46021)] and the review by this reviewer) on establishing equality of certain classes of operators and deciding on the question of complementability when the inclusions are proper. \par For $1 < p < \infty$, let $LC_p(X,\ell_{\infty})$ denote the space of operators that map weakly $p$-summable sequences to norm null sequences. When $X$ does not have the $p$-$L$-limited property, it is shown that the space of weakly compact operators $W(X,\ell_{\infty})$ is not complemented in $LC_p(X,\ell_{\infty})$.
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 7009314
zbMATH Keywords: limited $p$-convergence operators
zbMATH Keywords: $p$-Gelfand-Phillips property
zbMATH Keywords: $p$-$L$-limited property
author: Ioana Ghenciu
reviewed by: T.S.S.R.K. Rao
MaRDI profile type: Publication
OpenAlex ID: W2897277397
cites work: Complemented subspaces of linear bounded operators
cites work: Limited Operators and Strict Cosingularity
cites work: A stronger Dunford–Pettis property
cites work: Q4296471
cites work: Q3329946
cites work: Q4850055
cites work: Q4148368
cites work: Q3027659
cites work: Banach spaces in which Dunford-Pettis sets are relatively compact
cites work: On \(p\)-convergent operators on Banach lattices
cites work: DP*-properties of orderpon Banach spaces
cites work: \(L\)-sets and property \((SR^*)\) in spaces of compact operators
cites work: Q4596940
cites work: A note on Dunford-Pettis like properties and complemented spaces of operators
cites work: Completely continuous operators
cites work: Q3144656
cites work: Spaces of compact operators
cites work: Topological characterisation of weakly compact operators
cites work: The Gelfand-Phillips property in closed subspaces of some operator spaces
cites work: A new class of Banach spaces and its relation with some geometric properties of Banach spaces
cites work: Characterizations of Banach spaces with relatively compact Dunford-Pettis sets
Wikidata QID: Q128836586
DOI: 10.15352/AOT.1802-1318
description: scientific article; zbMATH DE number 7009314