Operadores de composición en algunos espacios de Hilbert de funciones analíticas

Vergara-Díaz, Fabrizzio M.

Publication

Operadores de composición en algunos espacios de Hilbert de funciones analíticas

Vergara-Díaz, Fabrizzio M.

Abstract

The operators of composition were studied by Carl Cowen, Barbara Maccluer [2] 1995 and Joel Shapiro [3] 1993. The operators of composition C' have the virtue that their properties are intimately related with the behavior of '. this allows the use classic results of the theory of analytic functions as well us contemporary results. In the work done, basic notions of the operator of composition are studied the main Hilbert space study is de Hardy space. It is seen how the composition operators act in this space. the conditions of compacity, like the condition of Hilbert Schmidt, the theory of weak convergence, the theory of univalent compacity, the relationship between the compacity, the univalence and the geometry of the automorphism of the disk D in which the theory of Julia Caratheodory and the theorem of Denjoy-Wol are studied. Finally, additional observations are made like the relationship between the Dirichlet spaces, the Hardy spaces and the Bergman spaces.