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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Automorphisms and tensor products of algebras


Author: John W. Bunce
Journal: Proc. Amer. Math. Soc. 44 (1974), 93-95
MSC: Primary 46H20
DOI: https://doi.org/10.1090/S0002-9939-1974-0331063-4
MathSciNet review: 0331063
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Abstract: In this note we prove that if $ A$ is a complex Banach algebra with identity, then the automorphism on $ A\hat \otimes A$ determined by $ \theta (a \otimes b) = b \otimes a$ is inner if and only if $ A = {M_n}(C)$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0331063-4
Keywords: Banach algebra, tensor product, automorphism
Article copyright: © Copyright 1974 American Mathematical Society