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


On isomorphic classifications of spaces of compact operators

Author: Elói Medina Galego
Journal: Proc. Amer. Math. Soc. 137 (2009), 3335-3342
MSC (2000): Primary 46B03, 46B25; Secondary 47B10
Published electronically: May 13, 2009
MathSciNet review: 2515403
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Abstract: We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces $ {\mathcal K}(X, Y^{\eta})$, $ \eta \geq \omega$, of compact operators from $ X$ to $ Y^{\eta}$, the space of all continuous $ Y$-valued functions defined in the interval of ordinals $ [1, \eta]$ and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces $ {\mathcal K}(X^{\xi}, c_{0}(\Gamma)^{\eta})$, where $ \omega \leq \xi < \omega_1$, $ \eta \geq \omega$, $ \Gamma$ is a countable set, $ X$ contains no complemented copy of $ l_1$, $ X^*$ has the Mazur property and the density character of $ X^{**}$ is less than or equal to $ \aleph_{1}$.

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Additional Information

Elói Medina Galego
Affiliation: Department of Mathematics, University of São Paulo, São Paulo, Brazil 05508-090

PII: S 0002-9939(09)09828-1
Keywords: Isomorphic classifications of spaces of continuous functions, compact operators
Received by editor(s): August 28, 2008
Published electronically: May 13, 2009
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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