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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.


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Article Information

TitleContinuity of operator-valued functions in the $*$-algebra of locally measurable operators
SourceMethods Funct. Anal. Topology, Vol. 20 (2014), no. 2, 124-133
MathSciNet MR3242861
zbMATH 1313.46066
MilestonesReceived 24/10/2013
CopyrightThe 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
Taurida National V. I. Vernadsky University, 4 Academician Vernadsky Ave., Simferopol, 95007, Ukraine


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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},
}


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