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Ring Isomorphisms of Banach Algebras

Published online by Cambridge University Press:  20 November 2018

Irving Kaplansky
Irving Kaplansky*
Affiliation:
University of Chicago
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In discussing an isomorphism between two Banach algebras, one will ordinarily tacitly assume that the mapping is linear (i.e., preserves the complex scalars as well as the ring operations). In general this cannot be avoided; for instance if the two Banach algebras are just the field of complex numbers, then the isomorphism is unrestricted, and could be given by any one of the myriads of discontinuous automorphisms of the complex numbers.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 374 - 381
Copyright
Copyright © Canadian Mathematical Society 1954

References

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