数学物理学报(英文版)

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COMPLETELY BOUNDED COHOMOLOGY OF NON-SELFADJOINT OPERATOR ALGEBRAS

侯成军; 魏翠萍   

  1. 曲阜师范大学数学系, 曲阜 273165
  • 收稿日期:2003-12-18 修回日期:2005-04-26 出版日期:2007-01-20 发布日期:2007-01-20
  • 通讯作者: 侯成军
  • 基金资助:

    Supported partially by NSF of China (10201007) and National Tianyuan Foundation of China (A0324614)

COMPLETELY BOUNDED COHOMOLOGY OF NON-SELFADJOINT OPERATOR ALGEBRAS

Hou Chengjun; Wei Cuiping   

  1. Department of Mathematics, Qufu Normal University, Qufu 273165, China
  • Received:2003-12-18 Revised:2005-04-26 Online:2007-01-20 Published:2007-01-20
  • Contact: Hou Chengjun

摘要:

The authors prove that all n-th completely bounded cohomology groups of a nest algebra $T({\cal N})$ acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed $T({\cal N})$-bimodule
containing the nest algebra. They also prove that $H_{cb}^n({\cal A},{\cal M})\cong H_{cb}^n({\cal A},{\cal A})$ for all $n\geq 1$ and a CSL algebra ${\cal A}$ with an ultraweakly closed ${\cal A}$-bimodule ${\cal M}$ containing ${\cal A}$.

关键词: Nest algebra, CSL algebra, completely bounded cohomology group

Abstract:

The authors prove that all n-th completely bounded cohomology groups of a nest algebra $T({\cal N})$ acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed $T({\cal N})$-bimodule
containing the nest algebra. They also prove that $H_{cb}^n({\cal A},{\cal M})\cong H_{cb}^n({\cal A},{\cal A})$ for all $n\geq 1$ and a CSL algebra ${\cal A}$ with an ultraweakly closed ${\cal A}$-bimodule ${\cal M}$ containing ${\cal A}$.

Key words: Nest algebra, CSL algebra, completely bounded cohomology group

中图分类号: 

  • 46H05