(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.
(This paper has appeared in Math. Proc. Cambridge Philos. Soc. 130 (2001), no. 1, 25--36)