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Spring 2008 Automorphisms of $\mathcal{C}(K)$-spaces and extension of linear operators
N. J. Kalton
Illinois J. Math. 52(1): 279-317 (Spring 2008). DOI: 10.1215/ijm/1242414132

Abstract

We study the class of separable (real) Banach spaces $X$ which can be embedded into a space $\mathcal{C}(K)$ ($K$ compact metric) in only one way up to automorphism. We show that in addition to the known spaces $c_0$ (and all it subspaces) and $ℓ_1$ (and all its weak*-closed subspaces) the space $c_{0}(ℓ_{1})$ has this property. We show on the other hand (answering a question of Castillo and Moreno) that $ℓ_p$ for $1 < p < ∞$ fails this property. We also show that $ℓ_p$ can be embedded in a super-reflexive space $X$ so that there is an operator $T : \ell_{p}\to\mathcal{C}(K)$ which has no extension, answering a question of Zippin.

Citation

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N. J. Kalton. "Automorphisms of $\mathcal{C}(K)$-spaces and extension of linear operators." Illinois J. Math. 52 (1) 279 - 317, Spring 2008. https://doi.org/10.1215/ijm/1242414132

Information

Published: Spring 2008
First available in Project Euclid: 15 May 2009

zbMATH: 1184.46010
MathSciNet: MR2507245
Digital Object Identifier: 10.1215/ijm/1242414132

Subjects:
Primary: 46B03, 46B20

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

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Vol.52 • No. 1 • Spring 2008
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