数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 995-1002.doi: 10.1016/S0252-9602(15)30033-3

• 论文 • 上一篇    下一篇

Lp-CONTINUITY OF NONCOMMUTATIVE CONDITIONAL EXPECTATIONS

胡建, 马聪变, 侯友良   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2014-07-25 修回日期:2015-01-26 出版日期:2015-09-01 发布日期:2015-09-01
  • 通讯作者: Congbian MA E-mail:macongbian@126.com
  • 作者简介:Jian HU, E-mail: hujian279@163.com; Congbian MA, E-mail: macongbian@126.com; Youliang HOU, E-mail: ylhou323@whu.edu.cn
  • 基金资助:

    This work was supported by National Natural Science Foundation of China (11271293, 11471251) and the Research Fund for the Doctoral Program of Higher Education of China (2014201020205).

Lp-CONTINUITY OF NONCOMMUTATIVE CONDITIONAL EXPECTATIONS

Jian HU, Congbian MA, Youliang HOU   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2014-07-25 Revised:2015-01-26 Online:2015-09-01 Published:2015-09-01
  • Contact: Congbian MA E-mail:macongbian@126.com
  • Supported by:

    This work was supported by National Natural Science Foundation of China (11271293, 11471251) and the Research Fund for the Doctoral Program of Higher Education of China (2014201020205).

摘要:

Let (M, τ) be a noncommutative probability space, (Mn)n≥1 a sequence of von Neumann subalgebras of M and N a von Neumann subalgebra of M. We introduce the notions of μ-approach and orthogonal approach for (Mn)n≥1 and prove that ε(x|Mn)ε(x|N) for any xLp(M) (1 ≤ p < ∞) if and only if (Mn)n≥1 τ-approaches and orthogonally approaches N.

关键词: von Neumann algebra, trace, conditional expectation, orthogonal approach

Abstract:

Let (M, τ) be a noncommutative probability space, (Mn)n≥1 a sequence of von Neumann subalgebras of M and N a von Neumann subalgebra of M. We introduce the notions of μ-approach and orthogonal approach for (Mn)n≥1 and prove that ε(x|Mn)ε(x|N) for any xLp(M) (1 ≤ p < ∞) if and only if (Mn)n≥1 τ-approaches and orthogonally approaches N.

Key words: von Neumann algebra, trace, conditional expectation, orthogonal approach

中图分类号: 

  • 46L51