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Commutants of certain multiplication operators on Hilbert spaces of analytic functions

K. SeddighiS. Vaezpour — 1999

Studia Mathematica

This paper characterizes the commutant of certain multiplication operators on Hilbert spaces of analytic functions. Let A = M z be the operator of multiplication by z on the underlying Hilbert space. We give sufficient conditions for an operator essentially commuting with A and commuting with A n for some n>1 to be the operator of multiplication by an analytic symbol. This extends a result of Shields and Wallen.

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