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

Abstract

In this paper we prove the existence of conditional expectations in the noncommutative $L_p(M,\Phi )$ 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 $L_p(M,\Phi )$ spaces.

16 pages. arXiv admin note: substantial text overlap with arXiv:1603.07812; text overlap with arXiv:1007.1878 by other authors

References in corpus (1)

• Weighted ergodic theorems for Banach-Kantorovich lattice $L_p(\hat{\nabla },\hat{\mu })$