Congruence of selfadjoint operators Given a bounded selfadjoint operator a in a Hilbert space $$\mathcal{H}$$ , the aim of this paper is to study the orbit of a, i.e., the set of operators which are congruent to a. We establish some necessary and sufficient conditions for an operator to be in the orbit of a. Also, the orbit of a selfadjoint operator with closed range is provided with a structure of differential manifold. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Positivity, Volume 13 (4) – Feb 6, 2009
12 pages

Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2267-y
Publisher site
See Article on Publisher Site

### Abstract

Given a bounded selfadjoint operator a in a Hilbert space $$\mathcal{H}$$ , the aim of this paper is to study the orbit of a, i.e., the set of operators which are congruent to a. We establish some necessary and sufficient conditions for an operator to be in the orbit of a. Also, the orbit of a selfadjoint operator with closed range is provided with a structure of differential manifold.

### Journal

PositivitySpringer Journals

Published: Feb 6, 2009

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