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, the C*-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 spaces A2(Ω) for a wide class of plane domains Ω⊂C, and in Fock spaces A2(CN), N≧1.
Citation
Miroslav Engliš. "Density of algebras generated by Toeplitz operators on Bergman spaces." Ark. Mat. 30 (1-2) 227 - 243, 1992. https://doi.org/10.1007/BF02384872
Information