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ISSN 1088-6826(e) ISSN 0002-9939(p)

A Kaplansky theorem for JB*-triples

Authors: Francisco J. Fernández-Polo, Jorge J. Garcés and Antonio M. Peralta
Journal: Proc. Amer. Math. Soc. 140 (2012), 3179-3191
MSC (2010): Primary 46K70, 46L05, 46L10, 46L70; Secondary 17C65
Posted: January 18, 2012
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Abstract | References | Similar Articles | Additional Information

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

has closed range whenever is continuous.
is bounded below if and only if 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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