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arXiv · 2402.00538

A Kaplansky Theorem for JB*-triples

Francisco J. Fernández-Polo·Jorge J. Garcés·Antonio M. Peralta
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Abstract

Let $T:E\rightarrow F$ be a non-necessarily continuous triple homomorphism from a (complex) JB$^*$-triple (respectively, a (real) J$^*$B-triple) to a normed Jordan triple. The following statements hold: (1) $T$ has closed range whenever $T$ is continuous (2) $T$ has closed range whenever $T$ is continuous This result generalises classical theorems of I. Kaplansky and S.B. Cleveland in the setting of C$^*$-algebras and of A. Bensebah and J.P\'erez, L. Rico and A. Rodr'\iguez Palacios in the setting of JB$^*$-algebras.

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Francisco J. Fernández-Polo, Jorge J. Garcés, Antonio M. Peralta. 2024-02-01. A Kaplansky Theorem for JB*-triples. https://doi.org/10.1090/s0002-9939-2012-11157-8

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