Holomorphic functions operating in Hermitian Banach algebras

El Kinani, A.

doi:10.1090/S0002-9939-1991-1055771-5

Holomorphic functions operating in Hermitian Banach algebras
HTML articles powered by AMS MathViewer

by A. El Kinani PDF

Proc. Amer. Math. Soc. 111 (1991), 931-939 Request permission

Abstract:

The purpose of this paper is to prove that Hermitian algebras are the natural framework for the results of Ky Fan on analytic functions of a proper contraction.

References

M. Akkar, A. El Kinani, and M. Oudadess, Calculus fonctionnels harmonique et analytique réel, Ann. Sci. Math. Québec 12 (1988), no. 2, 151–169 (French, with English summary). MR 978451
Robert S. Doran and Victor A. Belfi, Characterizations of $C^*$-algebras, Monographs and Textbooks in Pure and Applied Mathematics, vol. 101, Marcel Dekker, Inc., New York, 1986. The Gel′fand\mhy Naĭmark theorems. MR 831427
Ky Fan, Analytic functions of a proper contraction, Math. Z. 160 (1978), no. 3, 275–290. MR 482310, DOI 10.1007/BF01237041
Ky Fan, Sharpened forms of an inequality of von Neumann, Math. Z. 194 (1987), no. 1, 7–13. MR 871215, DOI 10.1007/BF01168002
Ciprian Foiaş, Sur certains théorèmes de J. von Neumann concernant les ensembles spectraux, Acta Sci. Math. (Szeged) 18 (1957), 15–20 (French). MR 90029
Gong Ning Chen, On simplified proofs of theorems of von Neumann, Heinz, and Ky Fan, and their extended versions, Nonlinear and convex analysis (Santa Barbara, Calif., 1985) Lecture Notes in Pure and Appl. Math., vol. 107, Dekker, New York, 1987, pp. 15–21. MR 892778

A note on Vitali’s convergence theorem

J. S. Hwang, A problem on the Riesz-Dunford operator calculus and convex univalent functions, Glasgow Math. J. 24 (1983), no. 2, 129–130. MR 706140, DOI 10.1017/S0017089500005188
Vlastimil Pták, Banach algebras with involution, Manuscripta Math. 6 (1972), 245–290. MR 296705, DOI 10.1007/BF01304613
Satish Shirali and James W. M. Ford, Symmetry in complex involutory Banach algebras. II, Duke Math. J. 37 (1970), 275–280. MR 261362
Mau Hsiang Shih and Kok-Keong Tan, Analytic functions of topological proper contractions, Math. Z. 187 (1984), no. 3, 317–323. MR 757473, DOI 10.1007/BF01161949