References
R. F. Arens, “Representations of *-algebras,”Duke Math. J.,14, 269–282 (1947);Proc. Natl. Acad. Sci. U.S.A.,32, 237–239 (1946).
B. Banaschewski, “The duality betweenM-spaces and compact Hausdorff spaces,”Math. Nachr.,75, 41–45 (1976).
F. F. Bonsall and J. Duncan,Complete Normed Algebras, Ergebnisse der Mathematik, No. 80, Springer-Verlag, Berlin (1973).
J. Dixmier,Les C *-algèbres et leurs représentations, Gauthier Villars, Paris (1969).
Normierte Ringe,Mat. Sb., N.S.,9, 3–24 (1941);Dokl. Akad. Nauk SSSR,23, 430–432 (1939).
I. M. Gel'fand and N. A. Naimark, “On the embedding of normed rings into the ring of operators in Hilbert space,”Mat. Sb., N.S.,12, 197–213 (1943).
L. Ingelstam, “Real Banach algebras,”Ark. för Mat.,5, 239–270 (1964).
J. R. Isbell,The unit ball of C(X) as an abstract algebra, Notes from lectures delivered at the Banach Center in Warsaw (1974).
J. Lambek and B. A. Rattray, “A general Stone-Gel'fand duality,”Trans. Amer. Math. Soc.,248, 1–35 (1979).
S. MacLane,Categories for the Working Mathematician, GTM5, Springer-Verlag, Berlin (1971).
A. Mallios,Topological Algebras. Selected Topics, Math. Stud., Vol. 124, North-Holland, Amsterdam (1986).
S. Mazur, “Sur les anneaux linéaires,”C. R. Acad. Sci. Paris, Ser. A-B,207, 1025–1027 (1938).
G. F. Nassopoulos, “Duality and functional representations of certain complete algebras,”Prakt. Akad. Athenon,56, 327–338 (1981).
G. F. Nassopoulos,The duality between locally C *-algebras and filtered spaces. Cambridge Summer Meeting in Category Theory, 1981.
H. E. Porst and M. B. Wischnewsky, “Every topological category is convenient for Gel'fand duality,”Manuscr. Math.,25, 169–204 (1978).
I. E. Segal, “Representation of certain commutative Banach algebras,”Bull. Amer. Math. Soc.,52, 421–422 (1946).
A. Sinclair,Automatic Continuity of Linear Operators, Lecture Notes Scries No. 21, London Math. Soc., London (1977).
I. M. Singer and J. Wermer, “Derivations on commutative nonned algebras,”Math. Ann.,129, 260–264 (1955).
M. H. Stone, “A general theory of spectra, I, II,”Proc. Natl. Acad. Sci. U.S.A.,26, 280–283 (1940);27, 83–87 (1941).
M. Takesaki,Theory of Operator Algebras, Springer-Verlag, Berlin (1979).
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 49, Functional Analysis-4, 1997.
Rights and permissions
About this article
Cite this article
Nassopoulos, G.F. On a comparison of real with complex involutive complete algebras. J Math Sci 96, 3755–3765 (1999). https://doi.org/10.1007/BF02172669
Issue Date:
DOI: https://doi.org/10.1007/BF02172669