Analytic Characterization for Hilbert-Schmidt Operators on Fock Space

作     者：Cai Shi WANG Zhi Yuan HUANG Xiang Jun WANG 

作者机构：School of Mathematics and Information Science Northwest Normal University Lanzhou 730070 P. R. China Department of Mathematics Huazhong University of Science & Technology Wuhan 430074 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2005年第21卷第4期

页      面：787-796页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(10171035) Natural Science Foundation of Gansu Province(ZS021-A25-004-Z) NWNU-KJCXGC-212 

主　　题：Fock space Hilbert-Schmidt operator Frěchet entire map 

摘      要：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.