On isomorphic classifications of spaces of compact operators
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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 $\aleph _{1}$.References
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Additional Information
- Elói Medina Galego
- Affiliation: Department of Mathematics, University of São Paulo, São Paulo, Brazil 05508-090
- MR Author ID: 647154
- Email: eloi@ime.usp.br
- Received by editor(s): August 28, 2008
- Published electronically: May 13, 2009
- Communicated by: Nigel J. Kalton
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3335-3342
- MSC (2000): Primary 46B03, 46B25; Secondary 47B10
- DOI: https://doi.org/10.1090/S0002-9939-09-09828-1
- MathSciNet review: 2515403