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Proceedings of the American Mathematical Society

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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
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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Guillermina Fongi
Affiliation: Instituto Argentino de Matemática, CONICET, Saavedra 15, 1083 Buenos Aires, Argentina

Alejandra Maestripieri
Affiliation: Instituto de Ciencias, Universidad Nacional General Sarmiento, 1613 Los Polvorines, Argentina

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.