Stabilité du spectre ponctuel d'opérateurs de Toeplitz généralisés
Tom 116 / 1995
Studia Mathematica 116 (1995), 1-22
DOI: 10.4064/sm-116-1-1-22
Streszczenie
A general scheme based on a commutation relation is proposed to give rise to a definition of generalized Toeplitz operators on a Banach space. Under suitable conditions the existence of a symbol is proved and its continuation to algebras generated by generalized Toeplitz operators is constructed. A stability theorem for the point spectrum of an operator from generalized Toeplitz algebras is established; as examples one considers the standard and operator valued Toeplitz operators on weighted Hardy spaces and on spaces of functions (distributions) with weighted $l^p$ Fourier transforms.
