Vol. 58, No. 1, 1975

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Jordan -homomorphisms between reduced Banach -algebras

Theodore Windle Palmer

Vol. 58 (1975), No. 1, 169–178

A number of known results on Jordan -homomorphism between B-algebras are generalized to Jordan -homomorphisms between reduced Banach *-algebras. However the main results presented here are new even for maps between B-algebras. We state these results briefly. For any -algebra A, let AqU be the set of quasi-unitary elements. Let A and B be reduced Banach -algebras ( = A-algebras). Let φ : A B be a linear map. Then φ is a Jordan *-homomorphism if and only if φ(AqU) BqU. If φ is bijective these conditions are equivalent to φ being a weakly positive isometry with respect to the Gelfand-Naimark norms of A and B.

Mathematical Subject Classification 2000
Primary: 46K05
Received: 11 December 1973
Published: 1 May 1975
Theodore Windle Palmer