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THE POSITION OF $\mathcal{K}(X,Y)$ IN $\mathcal{L}(X,Y)$

Published online by Cambridge University Press:  13 August 2013

DANIELE PUGLISI
DANIELE PUGLISI*
Affiliation:
Department of Mathematics and Computer Sciences, University of Catania, Catania 95125, Italy e-mail: [email protected]
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Abstract

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In this paper we investigate the nature of family of pairs of separable Banach spaces (X, Y) such that $\mathcal{K}(X,Y)$ is complemented in $\mathcal{L}(X,Y)$. It is proved that the family of pairs (X,Y) of separable Banach spaces such that $\mathcal{K}(X,Y)$ is complemented in $\mathcal{L}(X,Y)$ is not Borel, endowed with the Effros–Borel structure.

Keywords

Primary 46B20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 409 - 417
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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