Multiplicative functionals and entire functions

Krzysztof Jarosz

Studia Mathematica (1996)

  • Volume: 119, Issue: 3, page 289-297
  • ISSN: 0039-3223

Abstract

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Let A be a complex Banach algebra with a unit e, let T, φ be continuous functionals, where T is linear, and let F be a nonlinear entire function. If T ∘ F = F ∘ φ and T(e) = 1 then T is multiplicative.

How to cite

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Jarosz, Krzysztof. "Multiplicative functionals and entire functions." Studia Mathematica 119.3 (1996): 289-297. <http://eudml.org/doc/216301>.

@article{Jarosz1996,
abstract = {Let A be a complex Banach algebra with a unit e, let T, φ be continuous functionals, where T is linear, and let F be a nonlinear entire function. If T ∘ F = F ∘ φ and T(e) = 1 then T is multiplicative.},
author = {Jarosz, Krzysztof},
journal = {Studia Mathematica},
keywords = {multiplicative functionals; nonlinear entire function; multiplicative},
language = {eng},
number = {3},
pages = {289-297},
title = {Multiplicative functionals and entire functions},
url = {http://eudml.org/doc/216301},
volume = {119},
year = {1996},
}

TY - JOUR
AU - Jarosz, Krzysztof
TI - Multiplicative functionals and entire functions
JO - Studia Mathematica
PY - 1996
VL - 119
IS - 3
SP - 289
EP - 297
AB - Let A be a complex Banach algebra with a unit e, let T, φ be continuous functionals, where T is linear, and let F be a nonlinear entire function. If T ∘ F = F ∘ φ and T(e) = 1 then T is multiplicative.
LA - eng
KW - multiplicative functionals; nonlinear entire function; multiplicative
UR - http://eudml.org/doc/216301
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] T. W. Gamelin, Uniform Algebras, Chelsea, New York, 1984. 
  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] J.-P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339-343. Zbl0155.45803
  8. [8] G. Pólya and G. Szegö, Problems and Theorems in Analysis II, Springer, 1976. 
  9. [9] Z. Sawoń and A. Warzecha, On the general form of subalgebras of codimension 1 of Banach algebras with a unit, Studia Math. 29 (1968), 249-260. Zbl0157.20504
  10. [10] W. Żelazko, A characterization of multiplicative linear functionals in complex Banach algebras, ibid. 30 (1968), 83-85. Zbl0162.18504

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