Extending operators into Lindenstrauss spaces
type: Item
instance of: scholarly article
title: Extending operators into Lindenstrauss spaces
zbMATH Open document ID: 1165.46003
author: Jesús Suárez
author: Jesús M. F. Castillo
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
review text: \textit{J.\,Lindenstrauss} and \textit{A.\,Pełczyński} [J.~Funct.\ Anal.\ 8, 225--249 (1971; Zbl 0224.46041)] proved that every \(C(K)\)-valued operator from a subspace of \(c_{0}\) can be extended to the whole \(c_{0}\). In that paper,they also remarked that the same result is valid when replacing \(C(K)\)-spaces by ``isometric \(L_{1}\)-preduals'', henceforth called Lindenstrauss spaces. As its title suggests, the paper under review deals with extensions of operators into Lindenstrauss spaces. Among several deep results, the authors extend Lindenstrauss--Pełczyński's result to the nonseparable case and provide new constructions in which the extension of operators into Lindenstrauss spaces exists; for example, it is shown that the Bourgain--Pisier construction of \(\mathcal{L}_{\infty}\)-spaces [\textit{J.\,Bourgain} and \textit{G.\,Pisier}, Bol.\ Soc.\ Bras.\ Mat.\ 14, No.\,2, 109--123 (1983; Zbl 0586.46011)] is one of those.
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 5508731
zbMATH Keywords: extension of operators
zbMATH Keywords: Lindenstrauss spaces
zbMATH Keywords: \(L_{1}\)-preduals
reviewed by: Daniel Pellegrino
MaRDI profile type: Publication
full work available at URL: s11856-009-0001-5
OpenAlex ID: W2027881015
cites work: Separable G spaces are isomorphic to C(K) spaces
cites work: An M-space which is not isomorphic to a C(K) space
cites work: A predual of \(l_1\) which is not isomorphic to a C(K) space
cites work: A construction of ℒ∞-spaces and related Banach spacesand related Banach spaces
cites work: The long homology sequence for quasi-Banach spaces, with applications
cites work: Twisted sums with 𝐶(𝐾) spaces
cites work: Q3374335
cites work: Three-space problems in Banach space theory
cites work: On the Lindenstrauss-Rosenthal theorem
cites work: On Lindenstrauss–Pełczyński spaces
cites work: On essentially incomparable Banach spaces
cites work: Q5552458
cites work: Separable L\(_1\) preduals are quotients of C(\(\Delta\))
cites work: Extension of Operators from Subspaces of c 0 (Γ) into C(K) Spaces
cites work: Q4862948
cites work: Extension of linear operators and Lipschitz maps into \({\mathcal C}(K)\)-spaces
cites work: Automorphisms of \(\mathcal C(K)\)-spaces and extension of linear operators
cites work: Banach spaces whose duals are \(L_ 1\) spaces and their representing matrices
cites work: Contributions to the theory of the classical Banach spaces
cites work: Q4136031
cites work: On the classification of the Banach spaces whose duals are \(L_1\) spaces
cites work: Separable Banach spaces which admit \(I^ \infty_ n\) approximations
cites work: On automorphic Banach spaces
cites work: Q5612726
cites work: Inverse limits of compact spaces and direct limits of spaces of continuous functions
cites work: Some remarks on the Gurarij space
cites work: The embedding of Banach spaces into spaces with structure
cites work: Q3975982
cites work: Applications of Michael’s continuous selection theorem to operator extension problems
cites work: Q4440817
DOI: 10.1007/S11856-009-0001-5
description: scientific article; zbMATH DE number 5508731