Article
Composition Operators Whose Symbols Have Orthogonal Powers
Houston Journal of Mathematics
Document Type
Article
Publication Date
1-1-2011
Disciplines
Abstract
Composition operators on the Hilbert Hardy space H2 whose symbols are analytic selfmaps of the open unit disk having orthogonal powers are considered. The spectra and essential spectra of such operators are described. In the general case of an arbitrary analytic selfmap of the open unit disk, it is proved that the composition operator induced by that map has essential spectral radius less than 1 if and only if the map under consideration is a non–inner map with a fixed point in the unit disk. The canonical decomposition of a non–unitary composition contraction is determined.
Citation Information
Valentin Matache. "Composition Operators Whose Symbols Have Orthogonal Powers" Houston Journal of Mathematics Vol. 37 Iss. 3 (2011) p. 845 - 857 Available at: http://works.bepress.com/valentin-matache/20/