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On spaces of operators on $ C(Q)$ spaces ($ Q$ countable metric space)


Author: Christian Samuel
Journal: Proc. Amer. Math. Soc. 137 (2009), 965-970
MSC (2000): Primary 46B03, 46B25; Secondary 47B10
Published electronically: September 11, 2008
MathSciNet review: 2457436
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Abstract: In this paper we study spaces of nuclear operators $ {\mathcal N}(C(Q))$ and spaces of compact operators $ {\mathcal K}(C(Q))$ on spaces of continuous functions $ C(Q),$ where $ Q$ is a countable compact metric space, in connection with the C. Bessaga and A. Pełczyński isomorphic classification of these spaces.

We show that the spaces $ {\mathcal K}(C(Q))$ [resp. $ {\mathcal N}(C(Q))$] and $ {\mathcal K}(C(Q'))$ [resp. $ {\mathcal N}(C(Q'))$] are isomorphic if, and only if, $ C(Q)$ and $ C(Q')$ are isomorphic. We show also that $ {\mathcal N}(C(Q))$ is not isomorphic to a subspace of $ {\mathcal K}(C(Q)).$


References [Enhancements On Off] (What's this?)

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Additional Information

Christian Samuel
Affiliation: Centre National de la Recherche Scientifique UMR 6632, Université d’Aix- Marseille 3, 13397 Marseille Cedex 20, France
Email: christian.samuel@univ-cezanne.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09635-4
Keywords: Isomorphic classification of spaces of continuous functions, nuclear operators, compact operators
Received by editor(s): February 19, 2008
Published electronically: September 11, 2008
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society