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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Differential structure of the Thompson components of selfadjoint operators
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by Guillermina Fongi and Alejandra Maestripieri PDF
Proc. Amer. Math. Soc. 136 (2008), 613-622 Request permission

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
  • Received by editor(s): December 4, 2006
  • Published electronically: November 2, 2007
  • Communicated by: Joseph A. Ball
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2358503