In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each mini...In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a monomial.Furthermore,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)N.We also give some interesting examples.展开更多
By bounded vector-valued functions and block matrix representations of Hankel operators, we completely characterize the hyponormality of Toeplitz operators on the Hardy space of the polydisk.
文摘In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a monomial.Furthermore,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)N.We also give some interesting examples.
基金Supported by National Natural Science Foundation of China(Grant No.10971020)
文摘By bounded vector-valued functions and block matrix representations of Hankel operators, we completely characterize the hyponormality of Toeplitz operators on the Hardy space of the polydisk.
