In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator...In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.展开更多
A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schm...A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem.This paper proves that every finitely generated submodule M containing(z)-Φ(w)is Hilbert-Schmidt,where 0(z),p(w)are two finite Blaschke products.展开更多
The purpose of this paper is to generalize the (classical) Bochner theorem to the case where Radon probability measures are defined on the weak dual spaces of locally convex spaces. We also compare our result with oth...The purpose of this paper is to generalize the (classical) Bochner theorem to the case where Radon probability measures are defined on the weak dual spaces of locally convex spaces. We also compare our result with other topological descriptions of characteristic functionals of probability measures on other infinite dimensional spaces.展开更多
We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sutfficient conditions for such kind of weighted composition operators belo...We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sutfficient conditions for such kind of weighted composition operators belong to the Schatten-Von Neumann ideal Sp. As a corollary, we now have that Wφ,ψ is a Hilbert-Schmidt operator if and only if ∫Bn │ψ（w）│^2/（1-│φ（W）│^2）^n＋1 dV（W）〈∞展开更多
基金Supported by National Natural Science Foundation of China(10171035)Natural Science Foundation of Gansu Province(ZS021-A25-004-Z) NWNU-KJCXGC-212
文摘In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.
基金supported by the National Nature Science Foundation of China (Grant Nos.12031002,11971086)supported by the Dalian High-Level Talent Innovation Project (Grant No.2020RD09).
文摘A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem.This paper proves that every finitely generated submodule M containing(z)-Φ(w)is Hilbert-Schmidt,where 0(z),p(w)are two finite Blaschke products.
文摘The purpose of this paper is to generalize the (classical) Bochner theorem to the case where Radon probability measures are defined on the weak dual spaces of locally convex spaces. We also compare our result with other topological descriptions of characteristic functionals of probability measures on other infinite dimensional spaces.
基金the National Natural Science Foundation of China(10471039)the Natural Science Foundation of the Education Commission of Jiangsu Province(03KJD140210,06KJD110175)the Natural Science Foundation of Xuzhou Institute of Technology(KY200508).
文摘We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sutfficient conditions for such kind of weighted composition operators belong to the Schatten-Von Neumann ideal Sp. As a corollary, we now have that Wφ,ψ is a Hilbert-Schmidt operator if and only if ∫Bn │ψ（w）│^2/（1-│φ（W）│^2）^n＋1 dV（W）〈∞
基金supported by NSFC(No.10871224,No.11001159)the Fundamental Research Funds for the Central Universities(No.GK200902049,No.GK201002012)Scientific Research Program Funded by Shaanxi Provincial Education Department(No.11JK0475)
