数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 995-1002.doi: 10.1016/S0252-9602(15)30033-3
Lp-CONTINUITY OF NONCOMMUTATIVE CONDITIONAL EXPECTATIONS
胡建, 马聪变, 侯友良
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
Lp-CONTINUITY OF NONCOMMUTATIVE CONDITIONAL EXPECTATIONS
Jian HU, Congbian MA, Youliang HOU
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
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 x∈Lp(M) (1 ≤ p < ∞) if and only if (Mn)n≥1 τ-approaches and orthogonally approaches N.
中图分类号:
- 46L51