When is a linear functional multiplicative?
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- by M. Roitman and Y. Sternfeld PDF
- Trans. Amer. Math. Soc. 267 (1981), 111-124 Request permission
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.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 267 (1981), 111-124
- MSC: Primary 46H20; Secondary 16A99
- DOI: https://doi.org/10.1090/S0002-9947-1981-0621976-6
- MathSciNet review: 621976