Conditions of coincidence of central extensions of von Neumann algebras and algebras of measurable operators

Details Conditions of coincidence of central extensions of von Neumann algebras and algebras of measurable operators Conditions of coincidence of central extensions of von Neumann algebras and algebras of measurable operators

2011-10-21

arxiv.org/abs/1110.4779v1

Mathematics

Operator Algebras

14 pages

Scientific paper

Given a von Neumann algebra $M$ we consider the central extension $E(M)$ of
$M.$ We describe class of von Neumann algebras $M$ for which the algebra $E(M)$
coincides with the algebra $S(M)$ -- the algebra of all measurable operators
with respect to $M,$ and with $S(M, \tau)$ -- the algebra of all
$\tau$-measurable operators with respect to $M.$

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