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Toeplitz operators and algebras of bounded analytic functions on the disk

Published online by Cambridge University Press:  18 May 2009

R. C. Smith
R. C. Smith
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi 39762, USA
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Here and throughout, A is a closed subalgebra of H∞ that contains the disk algebra and M(A) denotes the maximal ideal space of A. Because A contains the function fo(z) = z, we can define the fiber Mλ(A) of M(A) for λ ε ∂D (the unit circle) in the usual way; i.e., Mλ(A) = {φ ∈ M(A): fo(φ) = λ}. The Bergman space of the unit disk D is the L2(D, dx dy)-closure of A. Let be the orthogonal projection. For f ∈ L∞(D, dx dy), define the multiplication operator Mf: L2(D, dx dy)→ L2, (D, dx dy) by

and define the Toeplitz operator by

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 2 , May 1991 , pp. 181 - 185
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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