# Banach principle in the space of τ-measurable operators

Michael Goldstein; Semyon Litvinov

Studia Mathematica (2000)

- Volume: 143, Issue: 1, page 33-41
- ISSN: 0039-3223

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topGoldstein, Michael, and Litvinov, Semyon. "Banach principle in the space of τ-measurable operators." Studia Mathematica 143.1 (2000): 33-41. <http://eudml.org/doc/216808>.

@article{Goldstein2000,

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.},

author = {Goldstein, Michael, Litvinov, Semyon},

journal = {Studia Mathematica},

keywords = {von Neumann algebra; faithful semifinite normal trace; complete lattice of all projections; closed operator; topological -algebra of all -measurable operators; bilateral almost uniform convergence; noncommutative Banach principle; noncommutative ergodic theorems},

language = {eng},

number = {1},

pages = {33-41},

title = {Banach principle in the space of τ-measurable operators},

url = {http://eudml.org/doc/216808},

volume = {143},

year = {2000},

}

TY - JOUR

AU - Goldstein, Michael

AU - Litvinov, Semyon

TI - Banach principle in the space of τ-measurable operators

JO - Studia Mathematica

PY - 2000

VL - 143

IS - 1

SP - 33

EP - 41

AB - 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.

LA - eng

KW - von Neumann algebra; faithful semifinite normal trace; complete lattice of all projections; closed operator; topological -algebra of all -measurable operators; bilateral almost uniform convergence; noncommutative Banach principle; noncommutative ergodic theorems

UR - http://eudml.org/doc/216808

ER -

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