Density of algebras generated by Toeplitz operators on Bergman spaces |
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Authors: | Miroslav Engli |
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Affiliation: | (1) Mathematical Institute, Czechoslovak Academy of Sciences, Žitná 25, 115 67 Prague 1, Czechoslovakia |
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Abstract: | In this paper it is shown that Toeplitz operators on Bergman space form a dense subset of the space of all bounded linear operators, in the strong operator topology, and that their norm closure contains all compact operators. Further, theC *-algebra generated by them does not contain all bounded operators, since all Toeplitz operators belong to the essential commutant of certain shift. The result holds in Bergman spacesA 2(Ω) for a wide class of plane domains Ω⊂C, and in Fock spacesA 2(C N),N≧1. |
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