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Compact Toeplitz operators with continuoussymbols on weighted Bergman spaces

Published online by Cambridge University Press:  07 August 2001

Takahiko Nakazi  and
Rikio Yoneda
Takahiko Nakazi
Affiliation:
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan
Rikio Yoneda
Affiliation:
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan
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Abstract

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Let L^2_a (D, d\sigma d\theta /2\pi ) be a complete weighted Bergman space on the open unit disc D, where d\sigma is a positive finite Borel measure on [0, 1). We show the following : when \phi is a continuous function on the closed unit disc \bar {D}, T_\phi is compact if and only if \phi = 0 on \partial D.

1991 Mathematics Subject Classification 47B35, 47B07.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 1 , March 2000 , pp. 31 - 35
Copyright
2000 Glasgow Mathematical Journal Trust