Compact and quasicompact homomorphisms between differentiable Lipschitz algebras
Mahyar, H. ; Sanatpour, A. H.
Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, p. 485-497 / Harvested from Project Euclid
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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.
Publié le : 2010-08-15
Classification:  Compact,  power compact,  quasicompact,  homomorphisms,  differentiable Lipschitz algebras,  46J15,  47B48 
@article{1284570734,
     author = {Mahyar, H. and Sanatpour, A. H.},
     title = {Compact and quasicompact homomorphisms between differentiable Lipschitz algebras},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 485-497},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1284570734}
}

Mahyar, H.; Sanatpour, A. H. Compact and quasicompact homomorphisms between differentiable Lipschitz algebras. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp.  485-497. http://gdmltest.u-ga.fr/item/1284570734/