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august 2010 Compact and quasicompact homomorphisms between differentiable Lipschitz algebras
H. Mahyar, A. H. Sanatpour
Bull. Belg. Math. Soc. Simon Stevin 17(3): 485-497 (august 2010). DOI: 10.36045/bbms/1284570734

Abstract

In this note we consider homomorphisms between differentiable Lipschitz algebras $Lip^n(X,\alpha)$ ($0<\alpha \leq 1$) and $lip^n(X,\alpha)$ ($0<\alpha <1$), where $X$ is a perfect compact plane set. We give sufficient conditions implying the compactness and power compactness of these homomorphisms. Moreover, we investigate under what conditions a quasicompact homomorphism between these algebras is power compact. We also give a necessary condition for a homomorphism between these algebras to be quasicompact and in certain cases to be power compact. Finally, using these results, by giving an example we show that there exists a quasicompact homomorphism between these algebras which is not power compact.

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H. Mahyar. A. H. Sanatpour. "Compact and quasicompact homomorphisms between differentiable Lipschitz algebras." Bull. Belg. Math. Soc. Simon Stevin 17 (3) 485 - 497, august 2010. https://doi.org/10.36045/bbms/1284570734

Information

Published: august 2010
First available in Project Euclid: 15 September 2010

zbMATH: 1213.47042
MathSciNet: MR2731370
Digital Object Identifier: 10.36045/bbms/1284570734

Subjects:
Primary: ‎46J15
Secondary: 47B48

Keywords: compact , differentiable Lipschitz algebras , homomorphisms , power compact , quasicompact

Rights: Copyright © 2010 The Belgian Mathematical Society

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Vol.17 • No. 3 • august 2010
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