Multiplicative functionals and entire functions, II

Krzysztof Jarosz

Studia Mathematica (1997)

  • Volume: 124, Issue: 2, page 193-198
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Jarosz, Krzysztof. "Multiplicative functionals and entire functions, II." Studia Mathematica 124.2 (1997): 193-198. <http://eudml.org/doc/216408>.

@article{Jarosz1997,
abstract = {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.},
author = {Jarosz, Krzysztof},
journal = {Studia Mathematica},
keywords = {Banach algebras; multiplicative functionals; entire functions},
language = {eng},
number = {2},
pages = {193-198},
title = {Multiplicative functionals and entire functions, II},
url = {http://eudml.org/doc/216408},
volume = {124},
year = {1997},
}

TY - JOUR
AU - Jarosz, Krzysztof
TI - Multiplicative functionals and entire functions, II
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 2
SP - 193
EP - 198
AB - 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.
LA - eng
KW - Banach algebras; multiplicative functionals; entire functions
UR - http://eudml.org/doc/216408
ER -

References

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  1. [1] R. Arens, On a theorem of Gleason, Kahane and Żelazko, Studia Math. 87 (1987), 193-196. Zbl0649.46044
  2. [2] C. Badea, The Gleason-Kahane-Żelazko theorem, Rend. Circ. Mat. Palermo Suppl. 33 (1993), 177-188. 
  3. [3] J. B. Conway, Functions of One Complex Variable, Grad. Texts in Math. 11, Springer, 1986. 
  4. [4] J. B. Conway, Functions of One Complex Variable II, Grad. Texts in Math. 159, Springer, 1995. 
  5. [5] A. M. Gleason, A characterization of maximal ideals, J. Anal. Math. 19 (1967), 171-172. Zbl0148.37502
  6. [6] K. Jarosz, Generalizations of the Gleason-Kahane-Żelazko theorem, Rocky Mountain J. Math. 21 (1991), 915-921. Zbl0781.46035
  7. [7] K. Jarosz, Multiplicative functionals and entire functions, Studia Math. 119 (1996), 289-297. Zbl0868.46037
  8. [8] J.-P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, ibid. 29 (1968), 339-343. Zbl0155.45803
  9. [9] W. Żelazko, A characterization of multiplicative linear functionals in complex Banach algebras, ibid. 30 (1968), 83-85. Zbl0162.18504

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