Artículos de revistas
The Essential Norm of Operators in the Toeplitz Algebra on Ap(Bn)
Fecha
2007-12Registro en:
Suarez, Fernando Daniel; The Essential Norm of Operators in the Toeplitz Algebra on Ap(Bn); Indiana University; Indiana University Mathematics Journal; 56; 5; 12-2007; 2185-2232
0022-2518
CONICET Digital
CONICET
Autor
Suarez, Fernando Daniel
Resumen
Let Ap be the Bergman space on the unit ball Bn of Cn for 1 <p< ∞, and Tp be the corresponding Toeplitz algebra. We show that every S ∈ Tp can be approximated by operators that are specially suited for the study of local behavior. This is used to obtain several estimates for the essential norm of S ∈ Tp, an estimate for the essential spectral radius of S ∈ T2, and a localization result for its essential spectrum. Finally, we characterize compactness in terms of the Berezin transform for operators in Tp.