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On a comparison of real with complex involutive complete algebras

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References

  1. R. F. Arens, “Representations of *-algebras,”Duke Math. J.,14, 269–282 (1947);Proc. Natl. Acad. Sci. U.S.A.,32, 237–239 (1946).

    Google Scholar 

  2. B. Banaschewski, “The duality betweenM-spaces and compact Hausdorff spaces,”Math. Nachr.,75, 41–45 (1976).

    Google Scholar 

  3. F. F. Bonsall and J. Duncan,Complete Normed Algebras, Ergebnisse der Mathematik, No. 80, Springer-Verlag, Berlin (1973).

    Google Scholar 

  4. J. Dixmier,Les C *-algèbres et leurs représentations, Gauthier Villars, Paris (1969).

    Google Scholar 

  5. Normierte Ringe,Mat. Sb., N.S.,9, 3–24 (1941);Dokl. Akad. Nauk SSSR,23, 430–432 (1939).

    Google Scholar 

  6. 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).

    Google Scholar 

  7. L. Ingelstam, “Real Banach algebras,”Ark. för Mat.,5, 239–270 (1964).

    Google Scholar 

  8. J. R. Isbell,The unit ball of C(X) as an abstract algebra, Notes from lectures delivered at the Banach Center in Warsaw (1974).

  9. J. Lambek and B. A. Rattray, “A general Stone-Gel'fand duality,”Trans. Amer. Math. Soc.,248, 1–35 (1979).

    Google Scholar 

  10. S. MacLane,Categories for the Working Mathematician, GTM5, Springer-Verlag, Berlin (1971).

    Google Scholar 

  11. A. Mallios,Topological Algebras. Selected Topics, Math. Stud., Vol. 124, North-Holland, Amsterdam (1986).

    Google Scholar 

  12. S. Mazur, “Sur les anneaux linéaires,”C. R. Acad. Sci. Paris, Ser. A-B,207, 1025–1027 (1938).

    Google Scholar 

  13. G. F. Nassopoulos, “Duality and functional representations of certain complete algebras,”Prakt. Akad. Athenon,56, 327–338 (1981).

    Google Scholar 

  14. G. F. Nassopoulos,The duality between locally C *-algebras and filtered spaces. Cambridge Summer Meeting in Category Theory, 1981.

  15. H. E. Porst and M. B. Wischnewsky, “Every topological category is convenient for Gel'fand duality,”Manuscr. Math.,25, 169–204 (1978).

    Google Scholar 

  16. I. E. Segal, “Representation of certain commutative Banach algebras,”Bull. Amer. Math. Soc.,52, 421–422 (1946).

    Google Scholar 

  17. A. Sinclair,Automatic Continuity of Linear Operators, Lecture Notes Scries No. 21, London Math. Soc., London (1977).

    Google Scholar 

  18. I. M. Singer and J. Wermer, “Derivations on commutative nonned algebras,”Math. Ann.,129, 260–264 (1955).

    Google Scholar 

  19. 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).

    Google Scholar 

  20. M. Takesaki,Theory of Operator Algebras, Springer-Verlag, Berlin (1979).

    Google Scholar 

Download references

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 49, Functional Analysis-4, 1997.

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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

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