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Commutants of Analytic Toeplitz Operators on the Bergman space

Summary: Commutants of Analytic Toeplitz Operators
on the Bergman space
Sheldon Axler, Ÿ
Zeljko Ÿ
CuŸckovi’c, N. V. Rao
31 July 1998
Abstract. In this note we show that if two Toeplitz operators on a Bergman
space commute and the symbol of one of them is analytic and nonconstant,
then the other one is also analytic.
Let# be a bounded open domain in the complex plane and let dA denote
area measure on ## The Bergman space L 2
a(## is the subspace of L
2(# , dA)
consisting of the square­integrable functions that are analytic on ## For a
bounded measurable function # on ## the Toeplitz operator T# with symbol
# is the operator on L 2
a(## defined by
T# (f) = P (#f),
where P is the orthogonal projection of L
2(# , dA) onto L 2


Source: Axler, Sheldon - Dean of the College of Science and Engineering, San Francisco State University


Collections: Mathematics