Toeplitz operators on Bergman spaces |
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Authors: | Nazih S Faour |
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Institution: | 1. Department of Mathematics, Kuwart University, P.O. Box 5969, KUWAIT CITY, KUWAIT
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Abstract: | Let ? be an element in \(H^\infty (D) + C(\overline D )\) such that ?* is locally sectorial. In this paper it is shown that the Toeplitz operator defined on the Bergman spaceA 2 (D) is Fredholm. Also, it is proved that ifS is an operator onA 2(D) which commutes with the Toeplitz operatorT ? whose symbol ? is a finite Blaschke product, thenS H ∞ (D) is contained inH ∞ (D). Moreover, some spectral properties of Toeplitz operators are discussed, and it is shown that the spectrum of a class of Toeplitz operators defined on the Bergman spaceA 2 (D), is not connected. |
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