Abstract
w x Sinclair and Tullo proved in 10 that Noetherian Banach algebras, that is, complex associative Banach algebras satisfying the ascending chain w x condition on left ideals, are finite-dimensional. In 4 , we extended this result to the alternative case. For a Jordan algebra, the natural Noetherian condition is the ascending chain condition on inner ideals. Here, we show that Noetherian Jordan Banach algebras are finite-dimensional.
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