Author:
BOUDI N.,MARHNINE H.,ZARHOUTI C.,FERNANDEZ LOPEZ A.,GARCIA RUS E.
Abstract
An associative or alternative algebra A is Noetherian if it satisfies the ascending
chain condition on left ideals. Sinclair and Tullo [21] showed that a complex
Noetherian Banach associative algebra is finite dimensional. This result was extended
by Benslimane and Boudi [5] to the alternative case.For a Jordan algebra J or a Jordan pair V, the suitable Noetherian condition is the
ascending chain condition on inner ideals. In a recent work Benslimane and Boudi
[6] proved that a complex Noetherian Banach Jordan algebra is finite dimensional.Here we show the following results:(i) the Jacobson radical of a Noetherian Banach Jordan pair is finite dimensional;(ii) nondegenerate Noetherian Banach Jordan pairs have finite capacity;(iii) complex Noetherian Banach Jordan pairs are finite dimensional.
Publisher
Cambridge University Press (CUP)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献