, Volume 13, Issue 4, pp 759–770 | Cite as

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.


Selfadjoint operators congruence of operators differential geometry 

Mathematics Subject Classification (2000)

Primary 47B15, 58B20 


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© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Instituto Argentino de MatemáticaCapital FederalArgentina
  2. 2.Facultad de IngenieríaCapital FederalArgentina

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