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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

When is a linear functional multiplicative?


Authors: M. Roitman and Y. Sternfeld
Journal: Trans. Amer. Math. Soc. 267 (1981), 111-124
MSC: Primary 46H20; Secondary 16A99
MathSciNet review: 621976
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Abstract: We prove here by elementary arguments a generalization of a theorem by Gleason, Kahane and Żelazko: If $ \varphi $ is a linear functional on an algebra with unit $ A$ such that $ \varphi (1) = 1$ and $ \varphi (u) \ne 0$ for any invertible $ u$ in $ A$, then $ \varphi $ is multiplicative, provided the spectrum of each element in $ A$ is bounded. We present also other conditions which may replace the assumptions on $ A$ in the theorem above.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0621976-6
PII: S 0002-9947(1981)0621976-6
Article copyright: © Copyright 1981 American Mathematical Society