Consider a von Neumann algebra M with a faithful normal semifinite trace τ. We prove that each order bounded sequence of τ-compact operators includes a subsequence whose arithmetic averages converge in τ. We also prove a ...
In this paper, we present new properties of the space L1(M, τ) of integrable (with respect to the trace τ) operators affiliated to a semifinite von Neumann algebra M. For self-adjoint τ-measurable operators A and B, we ...