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

### 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 $\mathcal{M}$.

Key words: Von Neumann algebra, locally measurable operator, local measure topology.

### Article Information

 Title Continuity of operator-valued functions in the $*$-algebra of locally measurable operators Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 2, 124-133 MathSciNet MR3242861 zbMATH 1313.46066 Milestones Received 24/10/2013 Copyright The Author(s) 2014 (CC BY-SA)

### Authors Information

V. I. Chilin
National University of Uzbekistan, Tashkent, 100174, Republic of Uzbekistan M. A. Muratov Taurida National

M. A. Muratov

### Citation Example

V. I. Chilin and M. A. Muratov, Continuity of operator-valued functions in the $*$-algebra of locally measurable operators, Methods Funct. Anal. Topology 20 (2014), no. 2, 124-133.

### BibTex

@article {MFAT719,
AUTHOR = {Chilin, V. I. and Muratov, M. A.},
TITLE = {Continuity of operator-valued functions in the $*$-algebra of locally measurable operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {2},
PAGES = {124-133},
ISSN = {1029-3531},
MRNUMBER = {MR3242861},
ZBLNUMBER = {1313.46066},
URL = {http://mfat.imath.kiev.ua/article/?id=719},
}