A remark on the containment of c0 in spaces of compact operators

Let X, Y be two Banach spaces. By L(X, Y) (resp. K(X, Y)) we denote the Banach space of all bounded, linear (resp. compact, bounded, linear) operators from X into Y. Several papers have been devoted to the question of when c0 embeds isomorphically into K(X, Y) (see 5, 8, 9 and their references) and...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 1992-03, Vol.111 (2), p.331-335
Main Author: Emmanuele, G.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
Online Access:Get full text
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Summary:Let X, Y be two Banach spaces. By L(X, Y) (resp. K(X, Y)) we denote the Banach space of all bounded, linear (resp. compact, bounded, linear) operators from X into Y. Several papers have been devoted to the question of when c0 embeds isomorphically into K(X, Y) (see 5, 8, 9 and their references) and its relationship with the following question: (i) is K(X, Y) always uncomplemented in L(X, Y) when L(X, Y)K(X, Y)?
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100075435