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Generalized Triple Homomorphisms and Derivations
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- Journal:
- Canadian Journal of Mathematics / Volume 65 / Issue 4 / 01 August 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 783-807
- Print publication:
- 01 August 2013
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- Article
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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.
