Compact operators on the weighted Bergman space A¹(ψ)

Tao Yu. "Compact operators on the weighted Bergman space A¹(ψ)." Studia Mathematica 177.3 (2006): 277-284. <http://eudml.org/doc/284906>.

@article{TaoYu2006,
abstract = {We show that a bounded linear operator S on the weighted Bergman space A¹(ψ) is compact and the predual space A₀(φ) of A¹(ψ) is invariant under S* if and only if $Sk_\{z\} → 0$ as z → ∂D, where $k_\{z\}$ is the normalized reproducing kernel of A¹(ψ). As an application, we give conditions for an operator in the Toeplitz algebra to be compact.},
author = {Tao Yu},
journal = {Studia Mathematica},
keywords = {weighted Bergman space; compact operator; Toeplitz operator; reproducing kernel; Toeplitz algebra},
language = {eng},
number = {3},
pages = {277-284},
title = {Compact operators on the weighted Bergman space A¹(ψ)},
url = {http://eudml.org/doc/284906},
volume = {177},
year = {2006},
}

TY - JOUR
AU - Tao Yu
TI - Compact operators on the weighted Bergman space A¹(ψ)
JO - Studia Mathematica
PY - 2006
VL - 177
IS - 3
SP - 277
EP - 284
AB - We show that a bounded linear operator S on the weighted Bergman space A¹(ψ) is compact and the predual space A₀(φ) of A¹(ψ) is invariant under S* if and only if $Sk_{z} → 0$ as z → ∂D, where $k_{z}$ is the normalized reproducing kernel of A¹(ψ). As an application, we give conditions for an operator in the Toeplitz algebra to be compact.
LA - eng
KW - weighted Bergman space; compact operator; Toeplitz operator; reproducing kernel; Toeplitz algebra
UR - http://eudml.org/doc/284906
ER -