
SIGMA 2 (2006), 023, 9 pages math.FA/0602441
http://dx.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 noncommutative 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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