Conditionally expectations and martingales in noncommutative L_p-spaces associated with center-valued traces

2016/03/29 by Inomjon Ganiev, Farrukh Mukhamedov
Mathematics · #math.FA #math.OA #msc:46L52 #msc:46L53

paper · pdf · doi:10.1016/s0252-9602(17)30055-3

published as Acta Mathematica Scientia, 37(2017,) 1019-1032 · 16 pages. arXiv admin note: substantial text overlap with arXiv:1603.07812; text overlap with arXiv:1007.1878 by other authors

arxiv created 2016/03/29 · arxiv updated 2017/08/15

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 the martingales in noncommutative L_p(M,Φ) spaces.

Citations

• Non-commutative L_p-spaces associated with a Maharam trace