Cohomology of a class of Kadison-Singer algebras

作     者：HOU ChengJun Institute of Operations Research, Qufu Normal University, Rizhao 276826, China 

作者机构：1. Institute of Operations Research Qufu Normal University Rizhao 276826 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2010年第53卷第7期

页      面：1824-1836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(Grant No. A0324614, 10971117) the Natural Science Foundation of Shandong Province (Grant No. Y2006A03,ZR2009AQ005) 

主　　题：Kadison-Singer algebra Kadison-Singer lattice nest algebra cohomology group 

摘      要：Let L be the complete lattice generated by a nest N on an infinite-dimensional separable Hilbert space H and a rank one projection P ξ given by a vector ξ in H. Assume that ξ is a separating vector for N , the core of the nest algebra Alg(N ). We show that L is a Kadison-Singer lattice, and hence the corresponding algebra Alg(L) is a Kadison-Singer algebra. We also describe the center of Alg(L) and its commutator modulo itself, and show that every bounded derivation from Alg(L) into itself is inner, and all n-th bounded cohomology groups H n (Alg(L), B(H)) of Alg(L) with coefficients in B(H) are trivial for all n≥1.