On Hahn-Banach extensions for certain operator ideals
type: Item
instance of: scholarly article
title: On Hahn-Banach extensions for certain operator ideals
zbMATH Open document ID: 0573.47042
DOI: 10.1007/BF01202499
author: Eugen Straeuli
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: Let \({\mathfrak A}\) be a closed ideal of operators between Banach spaces, and let Y and Z be Banach spaces with Y a closed subspace of Z. We exhibit an extensive class of ideals with the property that the Banach spaces X for which every \(S: Y\to X\) in \({\mathfrak A}\) may be extended to a \(\tilde S:\) \(Z\to X\) also in \({\mathfrak A}\), are precisely the \({\mathfrak L}_{\infty}\)- spaces with the Schur property. It is well known that the ideal of weakly compact operators belongs to this class. On the other hand, certain ideals, which are in a sense close to the ideal of weakly compact operators, do not belong to this class. In particular, we show that the ideal of Banach-Saks operators does not belong to this class by using specific properties of the Tsirelson space.
Mathematics Subject Classification ID: 47L10
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 3915051
zbMATH Keywords: operator ideals
zbMATH Keywords: extension properties
zbMATH Keywords: closed ideal of operators between Banach spaces
zbMATH Keywords: \({\mathfrak L}_{\infty }\)-spaces with the Schur property
zbMATH Keywords: ideal of weakly compact operators
zbMATH Keywords: ideal of Banach-Saks operators
zbMATH Keywords: Tsirelson space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3915051