Noetherian Banach Jordan pairs

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)

Subject

General Mathematics

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

1. A note on (ψ+,ψ−)-derivations of Banach–Jordan systems with nonzero socle;Asian-European Journal of Mathematics;2022-12-31

2. On Jordan Banach Algebras with Countably Generated Inner Ideals;Algebra Colloquium;2010-06

3. The Jordan algebras of a Lie algebra;Journal of Algebra;2007-02

4. Additive Derivations on Jordan Banach Pairs;Communications in Algebra;2004-12-31

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