Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 10, Number 2 (2019), 218-228.
A note on peripherally multiplicative maps on Banach algebras
Let and be complex Banach algebras, and let , and be surjective maps from onto . Denote by the boundary of the spectrum of . If is semisimple, has an essential socle, and for each , then we prove that the maps and coincide and are continuous Jordan isomorphisms. Moreover, if is prime with nonzero socle and and satisfy the aforementioned condition, then we show once again that the maps and coincide and are continuous. However, in this case we conclude that the maps are either isomorphisms or anti-isomorphisms. Finally, if is prime with nonzero socle and is a peripherally multiplicative map, then we prove that is continuous and either or is an isomorphism or an anti-isomorphism.
Ann. Funct. Anal., Volume 10, Number 2 (2019), 218-228.
Received: 22 April 2018
Accepted: 10 September 2018
First available in Project Euclid: 19 March 2019
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Schulz, Francois. A note on peripherally multiplicative maps on Banach algebras. Ann. Funct. Anal. 10 (2019), no. 2, 218--228. doi:10.1215/20088752-2018-0025. https://projecteuclid.org/euclid.afa/1552960866