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 as z → ∂D, where is the normalized reproducing kernel of A¹(ψ). As an application, we give conditions for an operator in the Toeplitz algebra to be compact.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-3-6,
author = {Tao Yu},
title = {Compact operators on the weighted Bergman space A$^1$($\psi$)},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {277-284},
zbl = {1122.47027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-3-6}
}
Tao Yu. Compact operators on the weighted Bergman space A¹(ψ). Studia Mathematica, Tome 173 (2006) pp. 277-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-3-6/