The Sarason＇s Toeplitz product problem asks when the Toeplitz product operator TuTv, with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the Fock-Sobolev space and have a complete solution that u = eq, v = Ce-q, where q is a linear complex polynomial and C is a nonzero constant.
In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.
We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equivalent conditions of Schatten p-class properties of Toeplitz operators by Berezin transform.
