Continuity of operator-valued functions in the $*$-algebra of locally measurable operators

Authors

  • M. A. Muratov National University of Uzbekistan, Tashkent, 100174, Republic of Uzbekistan M. A. Muratov Taurida National
  • V. I. Chilin Taurida National V. I. Vernadsky University, 4 Academician Vernadsky Ave., Simferopol, 95007, Ukraine

DOI:

Keywords:

Von Neumann algebra, locally measurable operator, local measure topology

Abstract

In the present paper we establish sufficient conditions for a complex-valued function $f$ defined on $\mathbb{R}$ which guarantee continuity of an operator-function $T\mapsto f(T)$ w.r.t. the topology of local measure convergence in the $*$-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated to a von Neumann algebra $\mathcal{M}$.

Downloads

Published

2014-06-25

Issue

Vol. 20 No. 2 (2014)

Section

Articles

How to Cite

Muratov, M. A., and V. I. Chilin. “Continuity of Operator-Valued Functions in the $*$-Algebra of Locally Measurable Operators”. Methods of Functional Analysis and Topology, vol. 20, no. 2, June 2014, pp. 124-33, https://zen.imath.kiev.ua/index.php/mfat/article/view/573.