Additive Derivations on Jordan Banach Pairs

Abstract

We show the invariance of “almost all” primitive ideals under additive derivations on a Jordan Banach pair and we extend the well known result of Johnson and Sinclair to the Jordan Banach pairs framework.

Key Words:

• Additive derivations
• Jordan Banach pairs
• Primitive ideals

Mathematics Subject Classification:

• 17C65
• 46H70
• 16W25

AcknowledgmentS

We express our gratitude to Professor Antonio Fernández López for his valuable comments and remarks and for Proposition 3.4. We also wish to thank Professor Ottmar Loos for the proof of Lemma 3.1. The first author wishes to express her thanks to A. Villena who drew her attention to the work of Laursen and Stein (1973). And we are really indebted to the referee for his valuable suggestions and comments. This work was partially supported by the proyect “Teoria de Lie y Teoria de espacios de Banach, Cadiz-Tetuan.”

Notes

^#Communicated by I. Shestakov.