A characterization of linear-multiplicative functionals in topological algebras

• Autorzy: Łuczak M.
• Języki publikacji: EN

Abstrakty

EN

The classical Gleason–Kahane–Zelazko theorem for complex Banach algebras was generalized for not necessary linear functionals by Kowalski and Słodkowski. We prove a version of the Kowalski–Słodkowski theorem for real Banach algebras and also for real and complex A-pseudoconvex algebras.

Słowa kluczowe

EN

A-pseudoconvex algebra; real algebra; Gleason-Kahane-Żelazko theorem; Kowalski-Słodkowski theorem

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2006
• Tom: Vol. 46, [Z] 1
• Strony: 79--91
• Opis fizyczny: bibliogr. 8 poz.

Twórcy

autor

Łuczak M.

• Koszalin University of Technology Department of Civil and Environmental Engineering, Division of Mathematics Sniadeckich 2, 75-453 Koszalin, Poland,

Bibliografia

• [1] F. F. Bonsall, J. Duncan, Complete Normed Algebras, Springer-Verlag, New York 1973.
• [2] A. M. Gleason, A characterization of maximal ideals, J. Analyse Math. 19 (1967), 171-172.
• [3] J.-P. Kahane, W. Zelazko, A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339-343.
• [4] S. Kowalski, Z. Słodkowski, A characterization of multiplicative linear functionals in Banach algebras, Studia Math. 67 (1980), 215-223.
• [5] S. H. Kulkarni, Gleason-Kahane-Zelazko theorem for real Banach algebras, Jour. Math. Phy. Sci. 18 (S) (1984), 19-28.
• [6] S. H. Kulkarni, B. V. Limaye, Real Function Algebras, Marcel Dekker, Inc., New York 1992.
• [7] M. Łuczak, On the Gleason-Kahane-Zelazko theorem, Comment. Math. Prace Mat. 44(2) (2004), 245-253.
• [8] W. Żelazko, A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math. 30 (1968), 83-85.