A Kaplansky theorem for JB*-triples

Fernández-Polo, Francisco; Garcés, Jorge; Peralta, Antonio

doi:10.1090/S0002-9939-2012-11157-8

A Kaplansky theorem for JB*-triples
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by Francisco J. Fernández-Polo, Jorge J. Garcés and Antonio M. Peralta PDF

Proc. Amer. Math. Soc. 140 (2012), 3179-3191 Request permission

Abstract:

Let $T:E\rightarrow F$ be a not necessarily continuous triple homomorphism from a (complex) JB$^*$-triple (respectively, a (real) J$^*$B-triple) to a normed Jordan triple. The following statements hold:

$T$ has closed range whenever $T$ is continuous.
$T$ is bounded below if and only if $T$ is a triple monomorphism.

This result generalises classical theorems of I. Kaplansky and S.B. Cleveland in the setting of C$^*$-algebras and of A. Bensebah and J. Pérez, L. Rico and A. Rodríguez Palacios in the setting of JB$^*$-algebras.

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