Takesaki-Takai Duality Theorem in Hilbert C^＊-Modules  

作　　者：Mao Zheng GUO Xiao Xia ZHANG 

机构地区：[1]LMAM [2]Department of Mathematics,Peking University [3]Department of Mathematics,Yantai University

出　　处：《Acta Mathematica Sinica,English Series》2004年第6期1079-1088,共10页数学学报（英文版）

基　　金：Supported by NSF 10301004,NSF 10171098;Yantai University PHD Foundation SX03B14

摘　　要：In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).

关 键 词：COACTION Crossed product Multiplicative unitary operator Hilbert C~*-module 

分 类 号：O177.5[理学—数学]