References
R. F. Arens andI. Kaplansky, Topological representations of algebras. Trans. Amer. Math. Soc.63, 457–481 (1948).
B. Aupetit, Charactérisation spectrale des algèbres de Banach commutatives. Pacific J. Math.63, 23–25 (1976).
B. Aupetit andJ. Zemánek, On the spectral radius in real Banach algebras. Bull. Acad. Polon. Sci. (12)26, 969–973 (1978).
F. F.Bonsall and J.Duncan, Complete normed algebras. Berlin-Heidelberg-New York 1973.
R. B. Burckel, A simpler proof of the commutative Glickfeld-Berkson Theorem. J. Lond.Math. Soc.2, 403–404 (1970).
P.Fijalkowski, Representation theorem for realB *-algebras. Bull. Soc. Sci. Lett. Lódz (2)34, (1984).
L. T. Gardner, An elementary proof of the Russo-Dye theorem. Proc. Amer. Math. Soc.90, 171 (1984).
K. R.Goodearl, Notes on Real and ComplexC *-algebras. Cheshire England and Boston 1982.
R. A. Hirschfeld andW. Zelazko, On spectral norm algebras. Bull. Acad. Polon. Sci, Sér. Sci. Math. Astronom. Phys.16, 195–199 (1968).
L. Ingelstam, Real Banach algebras. Ark. Mat.5, 239–279 (1964).
I. Kaplansky, Normed algebras. Duke Math. J.16, 399–418 (1949).
S. H. Kulkarni andB. V. Limaye, Gelfand-Naimark Theorems for Real Banach* algebras. Math. Japon.25, 545–558 (1980).
Le Page, Sur quelques conditions entraînant la commutativité dans les algébres de Banach. C. R. Acad. Sci. Paris, Sér A–B265, 235–237 (1967).
G. Niestegge, A note on criteria of Le Page and Hirschfeld-Zelasko for the commutativity of Banach algebras. Studia Math.79, 87–90 (1984).
V. Pták andJ. Zemánek, On uniform continuity of the spectral radius in Banach algebras. Manuscripta Math.20, 177–189 (1977).
C. E.Rickart, General Theory of Banach Algebras. Princeton 1960.
J. Zemánek, Spectral radius characterizations of commutativity in Banach algebras. StudiaMath.61, 257–268 (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Srivastav, A. Commutativity criteria for real Banach algebras. Arch. Math 54, 65–72 (1990). https://doi.org/10.1007/BF01190670
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01190670