Compact operators on the weighted Bergman space $A^1(\psi )$
Studia Mathematica, Tome 177 (2006) no. 3, pp. 277-284
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We show that a bounded linear operator $S$ on the weighted Bergman space $A^1(\psi )$ is compact and the predual space $A_0(\varphi )$ of $A^1(\psi )$ is invariant under $S^\ast $ if and only if $Sk_z \rightarrow 0$ as $z\rightarrow \partial D$, where $k_z$ is the normalized reproducing kernel of $A^1(\psi )$. As an application, we give conditions for an operator in the Toeplitz algebra to be compact.
Keywords:
bounded linear operator weighted bergman space psi compact predual space varphi psi invariant under ast only rightarrow rightarrow partial where normalized reproducing kernel psi application conditions operator toeplitz algebra compact
Affiliations des auteurs :
Tao Yu 1
@article{10_4064_sm177_3_6,
author = {Tao Yu},
title = {Compact operators on the weighted {Bergman} space $A^1(\psi )$},
journal = {Studia Mathematica},
pages = {277--284},
publisher = {mathdoc},
volume = {177},
number = {3},
year = {2006},
doi = {10.4064/sm177-3-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm177-3-6/}
}
Tao Yu. Compact operators on the weighted Bergman space $A^1(\psi )$. Studia Mathematica, Tome 177 (2006) no. 3, pp. 277-284. doi: 10.4064/sm177-3-6
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