
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 noncommutative version of the Banach
Principle for L^{∞}.
Key words:
von Neumann algebra; measure topology; almost uniform convergence; uniform equicontinuity; Banach principle.
pdf (205 kb)
ps (160 kb)
tex (13 kb)
References
 Bellow A., Jones R.L., A Banach principle for L^{∞}, Adv. Math., 1996, V.36, 155172.
 Bratelli O., Robinson D.N., Operator algebras and quantum statistical
mechanics, Berlin, Springer, 1979.
 Chilin V., Litvinov S., Uniform equicontinuity for sequences of homomorphisms
into the ring of measurable operators, Methods Funct. Anal.
Topology, submitted.
 Chilin V., Litvinov S., Skalski A., A few remarks in noncommutative
ergodic theory, J. Operator Theory, 2005, V.53, 301320.
 Goldstein M., Litvinov S.,
Banach principle in the space of tmeasurable operators,
Studia Math., 2000, V.143, 3341.
 Kadison R.V., A generalized Schwarz inequality and algebraic invariants
for operator algebras, Ann. of Math., 1952, V.56, 494503.
 Litvinov S., Mukhamedov F., On individual subsequential ergodic theorem
in von Neumann algebras, Studia Math., 2001, V.145, 5562.
 Nelson E., Notes on noncommutative integration, J. Funct. Anal., 1974, V.15, 103116.
 Segal I., A noncommutative extension of abstract integration, Ann. of Math., 1953, V.57, 401457.

