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On $\mu$-scale invariant operators


We introduce the concept of a $\mu$-scale invariant operator with respect to a unitary transformation in a separable complex Hilbert space. We show that if a nonnegative densely defined symmetric operator is $\mu$-scale invariant for some $\mu>0$, then both the Friedrichs and the Krein-von Neumann extensions of this operator are also $\mu$-scale invariant.

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TitleOn $\mu$-scale invariant operators
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 181-186
MathSciNet MR2336720
CopyrightThe Author(s) 2007 (CC BY-SA)

Authors Information

K. A. Makarov
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA

E. Tsekanovskii
Department of Mathematics, Niagara University, NY 14109, USA 

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K. A. Makarov and E. Tsekanovskii, On $\mu$-scale invariant operators, Methods Funct. Anal. Topology 13 (2007), no. 2, 181-186.


@article {MFAT416,
    AUTHOR = {Makarov, K. A. and Tsekanovskii, E.},
     TITLE = {On $\mu$-scale invariant operators},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {181-186},
      ISSN = {1029-3531},
       URL = {},

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