Cohomology of a class of Kadison-Singer algebras  

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

出　　处：《Science China Mathematics》2010年第7期1824-1836,共13页中国科学：数学（英文版）

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)

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.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.

关 键 词：Kadison-Singer ALGEBRA Kadison-Singer lattice NEST ALGEBRA COHOMOLOGY group 

分 类 号：O153[理学—数学]