SIGMA 2 (2006), 023, 9 pages      math.FA/0602441      https://doi.org/10.3842/SIGMA.2006.023

A Banach Principle for Semifinite von Neumann Algebras

Vladimir Chilin ^a and Semyon Litvinov ^b
a) Department of Mathematics, National University of Uzbekistan, Tashkent 700095, Uzbekistan
^b) Department of Mathematics, Pennsylvania State University, 76 University Drive, Hazleton, PA 18202, USA

Received November 25, 2005, in final form February 10, 2006; Published online February 20, 2006

Abstract
Utilizing the notion of uniform equicontinuity for sequences of functions with the values in the space of measurable operators, we present a non-commutative version of the Banach Principle for L^∞.

Key words: von Neumann algebra; measure topology; almost uniform convergence; uniform equicontinuity; Banach principle.

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