Banach principle in the space of τ-measurable operators
Volume 143 / 2000
Studia Mathematica 143 (2000), 33-41
DOI: 10.4064/sm-143-1-33-41
Abstract
We establish a non-commutative analog of the classical Banach Principle on the almost everywhere convergence of sequences of measurable functions. The result is stated in terms of quasi-uniform (or almost uniform) convergence of sequences of measurable (with respect to a trace) operators affiliated with a semifinite von Neumann algebra. Then we discuss possible applications of this result.
