Open Access

On $\mu$-scale invariant operators

Abstract

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.

Article Information

 Title On $\mu$-scale invariant operators Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 181-186 MathSciNet MR2336720 Copyright The 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

Citation Example

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

BibTex

@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 = {http://mfat.imath.kiev.ua/article/?id=416},
}