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.
@article{bwmeta1.element.bwnjournal-article-smv143i1p33bwm,
author = {Michael Goldstein and Semyon Litvinov},
title = {Banach principle in the space of $\tau$-measurable operators},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {33-41},
zbl = {0968.46049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv143i1p33bwm}
}
Goldstein, Michael; Litvinov, Semyon. Banach principle in the space of τ-measurable operators. Studia Mathematica, Tome 141 (2000) pp. 33-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv143i1p33bwm/
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