Essential Norm of Composition Operators on Banach Spaces of Hölder Functions. (28th November 2011)

• Record Type: Journal Article
• Authors: Jiménez-Vargas, A.; Lacruz, Miguel; Villegas-Vallecillos, Moisés
• Other Names: Reich Simeon Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2011(2011)
• Publication Date: 2011-11-28
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2011/590853
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Let( X, d ) be a pointed compact metric space, let0 < α < 1, and letφ : X → X be a base point preserving Lipschitz map. We prove that the essential norm of the composition operatorC φ induced by the symbolφ on the spaceslip 0 ( X, d α ) andLip 0 ( X, d α ) is given by the formula∥ C φ ∥ e = lim t → 0 sup 0 < d ( x, y ) < t (d ( φ ( x ), φ ( y ) ) α / d ( x, y ) α ) whenever the dual spacelip 0 ( X, d α ) ∗ has the approximation property. This happens in particular whenX is an infinite compact subset of a finite-dimensional normed linear space.