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Toeplitz operators on Bergman spaces

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Abstract

Let ϕ be an element in\(H^\infty (D) + C(\overline D )\) such that ϕ* 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 ϕ whose symbol ϕ 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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  1. Department of Mathematics, Kuwart University, P.O. Box 5969, KUWAIT CITY, KUWAIT

    Nazih S. Faour

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  1. Nazih S. Faour
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Faour, N.S. Toeplitz operators on Bergman spaces. Rend. Circ. Mat. Palermo 35, 221–232 (1986). https://doi.org/10.1007/BF02844733

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  • DOI: https://doi.org/10.1007/BF02844733

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