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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the extension of compact operators


Author: Ȧsvald Lima
Journal: Proc. Amer. Math. Soc. 64 (1977), 374-375
MSC: Primary 47B05; Secondary 46B05
MathSciNet review: 0448135
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Abstract: We prove that for a real Banach space A the following properties are equivalent:

(1) For every pair X, Y of Banach spaces such that $ X \subseteq Y$, every compact linear operator $ T:X \to A$ admits an almost normpreserving extension $ \tilde T:Y \to A$.

(2) The same as (1) but with $ \dim \, X = 2$ and $ Y = l_\infty ^3$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0448135-9
PII: S 0002-9939(1977)0448135-9
Article copyright: © Copyright 1977 American Mathematical Society