Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 023, 9 pages      math.FA/0602441

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

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.

pdf (205 kb)   ps (160 kb)   tex (13 kb)


  1. Bellow A., Jones R.L., A Banach principle for L, Adv. Math., 1996, V.36, 155-172.
  2. Bratelli O., Robinson D.N., Operator algebras and quantum statistical mechanics, Berlin, Springer, 1979.
  3. Chilin V., Litvinov S., Uniform equicontinuity for sequences of homomorphisms into the ring of measurable operators, Methods Funct. Anal. Topology, submitted.
  4. Chilin V., Litvinov S., Skalski A., A few remarks in non-commutative ergodic theory, J. Operator Theory, 2005, V.53, 301-320.
  5. Goldstein M., Litvinov S., Banach principle in the space of t-measurable operators, Studia Math., 2000, V.143, 33-41.
  6. Kadison R.V., A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann. of Math., 1952, V.56, 494-503.
  7. Litvinov S., Mukhamedov F., On individual subsequential ergodic theorem in von Neumann algebras, Studia Math., 2001, V.145, 55-62.
  8. Nelson E., Notes on non-commutative integration, J. Funct. Anal., 1974, V.15, 103-116.
  9. Segal I., A non-commutative extension of abstract integration, Ann. of Math., 1953, V.57, 401-457.

Previous article   Next article   Contents of Volume 2 (2006)