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Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space

Xing-Tang Dong;  Ze-Hua Zhou — 2013

Studia Mathematica

We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators T f T g on the harmonic Bergman space is equal to a Toeplitz operator T h , then the product T g T f is also the Toeplitz operator T h , and hence T f commutes with T g . From this we give necessary and sufficient conditions for the product of two Toeplitz operators, one quasihomogeneous and the other monomial, to be a Toeplitz operator.

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