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REDUCING SUBSPACES FOR A CLASS OF MULTIPLICATION OPERATORS

Published online by Cambridge University Press:  08 January 2001

KEHE ZHU
Affiliation:
Department of Mathematics, State University of New York, Albany, NY 12222, USA; kzhu@math.albany.edu
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Abstract

Let [ ] be the open unit disk in the complex plane [Copf ]. The Bergman space L2a([ ]) is the Hilbert space of analytic functions f in [ ] such that

formula here

where dA is the normalized area measure on [ ]. If

formula here

are two functions in L2a([ ]), then the inner product of f and g is given by

formula here

We study multiplication operators on L2a([ ]) induced by analytic functions. Thus for φ ∈ H ∞([ ]), the space of bounded analytic functions in [ ], we define

formula here

by

formula here

It is easy to check that Mφ is a bounded linear operator on L2a([ ]) with

formula here

Type
Research Article
Copyright
The London Mathematical Society 2000

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