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2017 Almost multiplicative linear functionals and entire functions
Ehsan Anjidani
Rocky Mountain J. Math. 47(1): 27-38 (2017). DOI: 10.1216/RMJ-2017-47-1-27

Abstract

Let $T$ be a unital, continuous linear functional defined on complex Banach algebra $A$. First, we prove an approximate version of the Gleason-Kahane-\.Zelazko theorem: given $\epsilon >0$, there exists an $M>0$ such that, if $$ T(\exp x)\neq 0,\quad x\in A,\ \|x\|\leq M, $$ then $T$ is $\epsilon $-almost multiplicative. Then, we show that this result remains true if the exponential function is replaced by a nonsurjective entire function~$F$ with $F'(0)\neq 0$.

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Ehsan Anjidani. "Almost multiplicative linear functionals and entire functions." Rocky Mountain J. Math. 47 (1) 27 - 38, 2017. https://doi.org/10.1216/RMJ-2017-47-1-27

Information

Published: 2017
First available in Project Euclid: 3 March 2017

zbMATH: 1371.46037
MathSciNet: MR3619756
Digital Object Identifier: 10.1216/RMJ-2017-47-1-27

Subjects:
Primary: 46H05
Secondary: 46H30, 46J05

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 1 • 2017
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