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Differential structure of the Thompson components of selfadjoint operators


Authors: Guillermina Fongi and Alejandra Maestripieri
Journal: Proc. Amer. Math. Soc. 136 (2008), 613-622
MSC (2000): Primary 47B15; Secondary 58B20
DOI: https://doi.org/10.1090/S0002-9939-07-09133-2
Published electronically: November 2, 2007
MathSciNet review: 2358503
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Abstract: Different equivalence relations are defined in the set $ L(\mathcal{H})^s$ of selfadjoint operators of a Hilbert space $ \mathcal{H}$ in order to extend a very well known relation in the cone of positive operators. As in the positive case, for $ a \in L(\mathcal{H})^s$ the equivalence class $ C_a$ admits a differential structure, which is compatible with a complete metric defined on $ C_a$. This metric coincides with the Thompson metric when $ a$ is positive.


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Additional Information

Guillermina Fongi
Affiliation: Instituto Argentino de Matemática, CONICET, Saavedra 15, 1083 Buenos Aires, Argentina
Email: fongig@fceia.unr.edu.ar

Alejandra Maestripieri
Affiliation: Instituto de Ciencias, Universidad Nacional General Sarmiento, 1613 Los Polvorines, Argentina
Email: amaestri@ungs.edu.ar

DOI: https://doi.org/10.1090/S0002-9939-07-09133-2
Keywords: Selfadjoint operators, Thompson part metric, differential geometry.
Received by editor(s): December 4, 2006
Published electronically: November 2, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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