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A Kaplansky Theorem for JB*-triples (2402.00538v1)
Published 1 Feb 2024 in math.OA and math.FA
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.