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ArticleOriginal scientific text

Title

Banach principle in the space of τ-measurable operators

Authors 1, 2

Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada
  2. Department of Mathematics, North Dakota State University, Fargo, ND 58105, U.S.A.

Abstract

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.

Bibliography

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Studia Mathematica
2000/143/1
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Pages:
33-41
Main language of publication
English
Received
1999-06-20
Accepted
2000-06-21
Published
2000
Exact and natural sciences