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Proceedings of the American Mathematical Society

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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
MathSciNet review: 0262833
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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.

References [Enhancements On Off] (What's this?)

  • [1] E. Bishop, Holomorphic completions, analytic continuation, and the interpolation of semi-norms, Ann. of Math. (2) 78 (1963), 468-500. MR 27 #4958. MR 0155016 (27:4958)
  • [2] A. Browder, Introduction to function algebras, Benjamin, New York, 1969. MR 39 #7431. MR 0246125 (39:7431)

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Keywords: Function algebra, Jensen inequality, multiplicative linear functional
Article copyright: © Copyright 1970 American Mathematical Society

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