Arkiv för Matematik
- Ark. Mat.
- Volume 30, Number 1-2 (1992), 227-243.
Density of algebras generated by Toeplitz operators on Bergman spaces
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.
Ark. Mat. Volume 30, Number 1-2 (1992), 227-243.
Received: 5 May 1991
First available in Project Euclid: 31 January 2017
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1992 © Institut Mittag-Leffler
Engliš, Miroslav. Density of algebras generated by Toeplitz operators on Bergman spaces. Ark. Mat. 30 (1992), no. 1-2, 227--243. doi:10.1007/BF02384872. https://projecteuclid.org/euclid.afm/1485898067