Commutants of certain multiplication operators on Hilbert spaces of analytic functions
Volume 133 / 1999
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.
