Multiplicative functionals and entire functions

• Autorzy: Krzysztof Jarosz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46J20: Ideals, maximal ideals, boundaries
• 46H30: Functional calculus in topological algebras
• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces
• 46H05: General theory of topological algebras
• 46J05: General theory of commutative topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 119
• Numer: 3
• Strony: 289-297

Daty

wydano

1996

otrzymano

1996-03-18

Twórcy

autor

Krzysztof Jarosz

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
• Southern Illinois University at Edwardsville, Edwardsville, Illinois 62026, U.S.A.

Bibliografia

• [1] R. Arens, On a theorem of Gleason, Kahane and Żelazko, Studia Math. 87 (1987), 193-196.
• [2] C. Badea, The Gleason-Kahane-Żelazko theorem, Rend. Circ. Mat. Palermo Suppl. 33 (1993), 177-188.
• [3] J. B. Conway, Functions of One Complex Variable, Grad. Texts in Math. 11, Springer, 1986.
• [4] T. W. Gamelin, Uniform Algebras, Chelsea, New York, 1984.
• [5] A. M. Gleason, A characterization of maximal ideals, J. Anal. Math. 19 (1967), 171-172.
• [6] K. Jarosz, Generalizations of the Gleason-Kahane-Żelazko theorem, Rocky Mountain J. Math. 21 (1991), 915-921.
• [7] J.-P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339-343.
• [8] G. Pólya and G. Szegö, Problems and Theorems in Analysis II, Springer, 1976.
• [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.
• [10] W. Żelazko, A characterization of multiplicative linear functionals in complex Banach algebras, ibid. 30 (1968), 83-85.