Complemented Copies of C₀ in Spaces of Compact Operators

We give a simple proof of a theorem of Cembranos, Saab and Saab to the effect that if X and Y are infinite dimensional Banach spaces, one of which contains a copy of c₀, then the injective tensor product$X\check{\otimes }Y$contains a complemented copy of c₀. We also extend the theorem to spaces of c...

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Bibliographic Details
Published in:Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences Vol. 91A; no. 2; pp. 239 - 241
Main Author: Ryan, Raymond A.
Format: Journal Article
Language:English
Published: Royal Irish Academy 01-01-1991
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Summary:We give a simple proof of a theorem of Cembranos, Saab and Saab to the effect that if X and Y are infinite dimensional Banach spaces, one of which contains a copy of c₀, then the injective tensor product$X\check{\otimes }Y$contains a complemented copy of c₀. We also extend the theorem to spaces of compact operators.
ISSN:0035-8975