Multiplicative properties of Jensen measures
Authors:
Takasi Itô and Bert M. Schreiber
Journal:
Proc. Amer. Math. Soc. 26 (1970), 305-306
MSC:
Primary 46.55
DOI:
https://doi.org/10.1090/S0002-9939-1970-0262833-5
MathSciNet review:
0262833
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Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that if $\psi$ is a linear functional on a function algebra with $\psi (1) = 1$, and if $\psi$ satisfies the Jensen inequality with respect to some finite nonnegative measure, then $\psi$ is multiplicative.
- Errett Bishop, Holomorphic completions, analytic continuation, and the interpolation of semi-norms, Ann. of Math. (2) 78 (1963), 468–500. MR 155016, DOI https://doi.org/10.2307/1970537
- Andrew Browder, Introduction to function algebras, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0246125
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Keywords:
Function algebra,
Jensen inequality,
multiplicative linear functional
Article copyright:
© Copyright 1970
American Mathematical Society