Commutants of certain multiplication operators on Hilbert spaces of analytic functions

Volume 133 / 1999

K Seddighi, S. M. Vaezpour Studia Mathematica 133 (1999), 121-130 DOI: 10.4064/sm-133-2-121-130

Abstract

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.

Authors

  • K Seddighi
  • S. M. Vaezpour

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