An associative or alternative algebra A is Noetherian if it satisfies the ascending
chain condition on left ideals. Sinclair and Tullo  showed that a complex
Noetherian Banach associative algebra is finite dimensional. This result was extended
by Benslimane and Boudi  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
 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.