Vol. 58, No. 1, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Jordan -homomorphisms between reduced Banach -algebras

Theodore Windle Palmer

Vol. 58 (1975), No. 1, 169–178
Abstract

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
Milestones
Received: 11 December 1973
Published: 1 May 1975
Authors
Theodore Windle Palmer