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Essential norm of composition operators on Banach spaces of Hölder functions

Opened Access Essential norm of composition operators on Banach spaces of Hölder functions

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Autor: Villegas Vallecillos, Moisés
Lacruz Martín, Miguel Benito
Jiménez Vargas, Antonio
Fecha: 2011
Publicado en: Abstract and Applied Analysis, 2011, 590853-1-590853-13.
Tipo de documento: Artículo
Resumen: Let (X, d) be a pointed compact metric space, let 0 < α < 1, and let ϕ : X → X be a base point-preserving Lipschitz map. We show that the essential norm of the composition operator Cϕ induced by the symbol ϕ on the Lipschitz spaces lip0 (X, dα) and Lip0(X, dα) is given by the formula kCϕke = lim t→0 sup 0<d(x,y)<t d(ϕ(x), ϕ(y))α d(x, y) α whenever the dual space lip0 (X, dα)∗ has the approximation property. This happens in particular when X is an infinite compact subset of a finite-dimensional normed linear space.
Cita: Villegas Vallecillos, M., Lacruz Martín, M.B. y Jiménez Vargas, A. (2011). Essential norm of composition operators on Banach spaces of Hölder functions. Abstract and Applied Analysis, 2011, 590853-1-590853-13.
Tamaño: 1.857Mb
Formato: PDF

URI: http://hdl.handle.net/11441/16101

DOI: 10.1155/2011/590853

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