Let A be a complex Banach algebra with a unit e, let F be a nonconstant entire function, and let T be a linear functional with T(e)=1 and such that T∘F: A → ℂ is nonsurjective. Then T is multiplicative.
@article{bwmeta1.element.bwnjournal-article-smv124i2p193bwm,
author = {Krzysztof Jarosz},
title = {Multiplicative functionals and entire functions, II},
journal = {Studia Mathematica},
volume = {122},
year = {1997},
pages = {193-198},
zbl = {0897.46036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv124i2p193bwm}
}
Jarosz, Krzysztof. Multiplicative functionals and entire functions, II. Studia Mathematica, Tome 122 (1997) pp. 193-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv124i2p193bwm/
[00000] [1] R. Arens, On a theorem of Gleason, Kahane and Żelazko, Studia Math. 87 (1987), 193-196. | Zbl 0649.46044
[00001] [2] C. Badea, The Gleason-Kahane-Żelazko theorem, Rend. Circ. Mat. Palermo Suppl. 33 (1993), 177-188.
[00002] [3] J. B. Conway, Functions of One Complex Variable, Grad. Texts in Math. 11, Springer, 1986.
[00003] [4] J. B. Conway, Functions of One Complex Variable II, Grad. Texts in Math. 159, Springer, 1995.
[00004] [5] A. M. Gleason, A characterization of maximal ideals, J. Anal. Math. 19 (1967), 171-172. | Zbl 0148.37502
[00005] [6] K. Jarosz, Generalizations of the Gleason-Kahane-Żelazko theorem, Rocky Mountain J. Math. 21 (1991), 915-921. | Zbl 0781.46035
[00006] [7] K. Jarosz, Multiplicative functionals and entire functions, Studia Math. 119 (1996), 289-297. | Zbl 0868.46037
[00007] [8] J.-P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, ibid. 29 (1968), 339-343. | Zbl 0155.45803
[00008] [9] W. Żelazko, A characterization of multiplicative linear functionals in complex Banach algebras, ibid. 30 (1968), 83-85. | Zbl 0162.18504