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Generalized Triple Homomorphisms and Derivations

Published online by Cambridge University Press:  20 November 2018

Jorge J. Garcés
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, e-mail: [email protected], [email protected]
Antonio M. Peralta
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, e-mail: [email protected], [email protected]
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Abstract

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We introduce generalized triple homomorphisms between Jordan–Banach triple systems as a concept that extends the notion of generalized homomorphisms between Banach algebras given by K. Jarosz and B. E. Johnson in 1985 and 1987, respectively. We prove that every generalized triple homomorphism between $\text{J}{{\text{B}}^{*}}$-triples is automatically continuous. When particularized to ${{C}^{*}}$-algebras, we rediscover one of the main theorems established by Johnson. We will also consider generalized triple derivations from a Jordan–Banach triple $E$ into a Jordan–Banach triple $E$-module, proving that every generalized triple derivation from a $\text{J}{{\text{B}}^{*}}$-triple $E$ into itself or into ${{E}^{*}}$is automatically continuous.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2013

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