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.
Citation
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
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