On the setting of the unit ball U the author considers Toeplitz operators on Bergman space.The Bergman space Bp(U) (1≤ p < ∞) is the closed subspace of the usual Lebesgue space LP(U) consisting of holomorphic fun...On the setting of the unit ball U the author considers Toeplitz operators on Bergman space.The Bergman space Bp(U) (1≤ p < ∞) is the closed subspace of the usual Lebesgue space LP(U) consisting of holomorphic functions. For a function β ∈ L2(U), the Toeplitz operator Tβ with symbol β is defined by Tβf = (βf) for function f ∈ B2(U). Here is the Bergman projection from L2(U) onto B2(U). Two bounded linear operators S, T on the Hilbert H are said to be essentially commuting on H if the commutator ST - TS is compact on H. In this paper, a criterion of essentially Toeplitz operators with the vanishing property is obtained.展开更多
文摘On the setting of the unit ball U the author considers Toeplitz operators on Bergman space.The Bergman space Bp(U) (1≤ p < ∞) is the closed subspace of the usual Lebesgue space LP(U) consisting of holomorphic functions. For a function β ∈ L2(U), the Toeplitz operator Tβ with symbol β is defined by Tβf = (βf) for function f ∈ B2(U). Here is the Bergman projection from L2(U) onto B2(U). Two bounded linear operators S, T on the Hilbert H are said to be essentially commuting on H if the commutator ST - TS is compact on H. In this paper, a criterion of essentially Toeplitz operators with the vanishing property is obtained.
