Differential structure of the Thompson components of selfadjoint operators

Fongi, Guillermina; Maestripieri, Alejandra

doi:10.1090/S0002-9939-07-09133-2

Differential structure of the Thompson components of selfadjoint operators
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by Guillermina Fongi and Alejandra Maestripieri

Proc. Amer. Math. Soc. 136 (2008), 613-622

DOI: https://doi.org/10.1090/S0002-9939-07-09133-2

Published electronically: November 2, 2007

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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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