Geodesic
The Gleason-Kahane-Zelazko theorem and function algebras
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 2, pp. 87-108.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

A theorem due to A. Gleason, J.-P. Kahane and W. Zelazko characterizes continuous characters within the space of all continuous linear forms of a locally multiplicatively convex, sequentially complete algebra. The present paper applies these results to investigate linear isometries of Banach algebras (with particular attention to normal uniform algebras) and of some locally multiplicatively convex algebras. The locally multiplicatively convex algebra of all holomorphic functions on a domain, will be investigated at the end of the paper.
Un teorema dovuto a A. Gleason, J.-P. Kahane e W. Zelazko determina i caratteri continui nello spazio di tutte le forme lineari continue di un'algebra moltiplicativamente localmente convessa e sequenzialmente completa. Nel presente lavoro si applicano questi risultati allo studio delle isometrie lineari di algebre di Banach (con particolare attenzione alle algebre normali uniformi) e di algebre localmente moltiplicativamente convesse. Si studia infine l'algebra localmente moltiplicativamente convessa delle funzioni olomorfe su un dominio. 
@article{RLIN_2005_9_16_2_a1,
     author = {Vesentini, Edoardo},
     title = {The {Gleason-Kahane-Zelazko} theorem and function algebras},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {87--108},
     publisher = {mathdoc},
     volume = {Ser. 9, 16},
     number = {2},
     year = {2005},
     zbl = {1225.46040},
     mrnumber = {1957004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_2_a1/}
}
TY  - JOUR
AU  - Vesentini, Edoardo
TI  - The Gleason-Kahane-Zelazko theorem and function algebras
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 2005
SP  - 87
EP  - 108
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_2_a1/
LA  - en
ID  - RLIN_2005_9_16_2_a1
ER  - 
%0 Journal Article
%A Vesentini, Edoardo
%T The Gleason-Kahane-Zelazko theorem and function algebras
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 2005
%P 87-108
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_2_a1/
%G en
%F RLIN_2005_9_16_2_a1
Vesentini, Edoardo. The Gleason-Kahane-Zelazko theorem and function algebras. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 2, pp. 87-108. http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_2_a1/

[1] R.J. Fleming - J.E. Jamison, Isometries on Banach spaces: function spaces. Chapman and Hall/CRC Press, Boca Raton, Florida, 2002, 208 pp. | MR | Zbl

[2] A. Gleason, A characterization of maximal ideals. J. Analyse Math., 19, 1967, 171-172. | MR | Zbl

[3] K. Hoffman, Banach spaces of analytic functions. Prentice-Hall Series in Modern Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1962, 217 pp. | MR | Zbl

[4] W. Holsztyński, Continuous mappings induced by isometries of spaces of continuous functions. Studia Math., 26, 1966, 133-136. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[5] L. Hörmander, An introduction to complex analysis in several variables. Van Nostrand, Princeton, N.J., 1966, 208 pp. | MR | Zbl

[6] J.-P. Kahane - W. Zelazko, A characterization of maximal ideals in commutative Banach algebras. Studia Math., 29, 1968, 339-343. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[7] H. Kamowitz - S. Scheinberg, The spectrum of automorphisms of Banach algebras. J. Functional Analysis, 4, 1949, 268-276. | MR | Zbl

[8] A. Martineau, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel. J. Analyse Math., 9, 1963, 1-164. | MR | Zbl

[9] E. Michael, Locally multiplicatively-convex topological algebras. Mem. Amer. Math. Soc., 11, 1952, 82 pp. | MR | Zbl

[10] M. Nagasawa, Isomorphisms between commutative Banach algebras with an application to rings of analytic functions. Kodai Math. Sem. Rep., 11, 1959, 182-188. | fulltext mini-dml | MR | Zbl

[11] C.E. Rickart, General theory of Banach algebras. Van Nostrand, Princeton, N.J., 1960. | MR | Zbl

[12] W. Rudin, Functional analysis. McGraw Hill, New York 1973. | MR | Zbl

[13] S. Scheinberg, Automorphisms of commutative Banach algebras. In: R.C. GUNNING (ed.), Problems in analysis. A symposium in honor of Salomon Bochner. Princeton University Press, Princeton, N.J., 1970, 319-323. | MR | Zbl

[14] E. Vesentini, On the Banach-Stone Theorem. Advances in Math., 112, 1995, 135-146. | DOI | MR | Zbl

[15] E. Vesentini, Weighted composition operators and the Gleason-Kahane-Zelazko theorem. Advances in Math., 191, 2005, 423-445. | DOI | MR | Zbl

[16] E. Vesentini, Introduction to continuous semigroups. Scuola Normale Superiore, Pisa 2002. | MR | Zbl

[17] W. Zelazko, A characterization of multiplicative linear functionals in complex Banach algebras. Studia Math., 29, 1968, 339-343. | fulltext EuDML | fulltext mini-dml | MR | Zbl