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Toeplitz Operators on Bergman Spaces

Published online by Cambridge University Press:  20 November 2018

Sheldon Axler ,
John B. Conway  and
Gerard McDonald
Sheldon Axler
Affiliation:
Michigan State University, East Lansing, Michigan
John B. Conway
Affiliation:
Indiana University, Bloomington, Indiana
Gerard McDonald
Affiliation:
Western Illinois University, Macomb, Illinois
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Let G be a bounded, open, connected, non-empty subset of the complex plane C. We put the usual two dimensional (Lebesgue) area measure on G and consider the Hilbert space L2(G) that consists of the complex-valued, measurable functions defined on G that are square integrable. The inner product on L2(G) is given by the norm ‖h‖2 of a function h in L2(G) is given by ‖h‖2 = (∫G|h|2)1/2.

The Bergman space of G, denoted La2(G), is the set of functions in L2(G) that are analytic on G. The Bergman space La2(G) is actually a closed subspace of L2(G) (see [12 , Section 1.4]) and thus it is a Hilbert space.

Let G denote the closure of G and let C(G) denote the set of continuous, complex-valued functions defined on G.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 2 , 01 April 1982 , pp. 466 - 483
Copyright
Copyright © Canadian Mathematical Society 1982

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