CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE Lp-SPACES ASSOCIATED WITH CENTER-VALUED TRACES

doi:10.1016/S0252-9602(17)30055-3

Abstract

Abstract:

In this paper we prove the existence of conditional expectations in the noncommutative L_p(M, Φ)-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative L_p(M, Φ)-spaces.

Key words: noncommutative L_p(M, Φ)-space, Banach-Kantorovich space, measurable, conditional expectation, measurable bundle, martingale

Inomjon GANIEV, Farrukh MUKHAMEDOV. CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE L_p-SPACES ASSOCIATED WITH CENTER-VALUED TRACES[J].Acta mathematica scientia,Series B, 2017, 37(4): 1019-1032.

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CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE L_p-SPACES ASSOCIATED WITH CENTER-VALUED TRACES

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