Acta mathematica scientia, Series B >
Lp-CONTINUITY OF NONCOMMUTATIVE CONDITIONAL EXPECTATIONS
Received date: 2014-07-25
Revised date: 2015-01-26
Online published: 2015-09-01
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).
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.
Key words： von Neumann algebra; trace; conditional expectation; orthogonal approach
Jian HU , Congbian MA , Youliang HOU . Lp-CONTINUITY OF NONCOMMUTATIVE CONDITIONAL EXPECTATIONS[J]. Acta mathematica scientia, Series B, 2015 , 35(5) : 995 -1002 . DOI: 10.1016/S0252-9602(15)30033-3
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