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Commutativity criteria for real Banach algebras

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References

  1. R. F. Arens andI. Kaplansky, Topological representations of algebras. Trans. Amer. Math. Soc.63, 457–481 (1948).

    Google Scholar 

  2. B. Aupetit, Charactérisation spectrale des algèbres de Banach commutatives. Pacific J. Math.63, 23–25 (1976).

    Google Scholar 

  3. B. Aupetit andJ. Zemánek, On the spectral radius in real Banach algebras. Bull. Acad. Polon. Sci. (12)26, 969–973 (1978).

    Google Scholar 

  4. F. F.Bonsall and J.Duncan, Complete normed algebras. Berlin-Heidelberg-New York 1973.

  5. R. B. Burckel, A simpler proof of the commutative Glickfeld-Berkson Theorem. J. Lond.Math. Soc.2, 403–404 (1970).

    Google Scholar 

  6. P.Fijalkowski, Representation theorem for realB *-algebras. Bull. Soc. Sci. Lett. Lódz (2)34, (1984).

  7. L. T. Gardner, An elementary proof of the Russo-Dye theorem. Proc. Amer. Math. Soc.90, 171 (1984).

    Google Scholar 

  8. K. R.Goodearl, Notes on Real and ComplexC *-algebras. Cheshire England and Boston 1982.

  9. R. A. Hirschfeld andW. Zelazko, On spectral norm algebras. Bull. Acad. Polon. Sci, Sér. Sci. Math. Astronom. Phys.16, 195–199 (1968).

    Google Scholar 

  10. L. Ingelstam, Real Banach algebras. Ark. Mat.5, 239–279 (1964).

    Google Scholar 

  11. I. Kaplansky, Normed algebras. Duke Math. J.16, 399–418 (1949).

    Google Scholar 

  12. S. H. Kulkarni andB. V. Limaye, Gelfand-Naimark Theorems for Real Banach* algebras. Math. Japon.25, 545–558 (1980).

    Google Scholar 

  13. Le Page, Sur quelques conditions entraînant la commutativité dans les algébres de Banach. C. R. Acad. Sci. Paris, Sér A–B265, 235–237 (1967).

    Google Scholar 

  14. G. Niestegge, A note on criteria of Le Page and Hirschfeld-Zelasko for the commutativity of Banach algebras. Studia Math.79, 87–90 (1984).

    Google Scholar 

  15. V. Pták andJ. Zemánek, On uniform continuity of the spectral radius in Banach algebras. Manuscripta Math.20, 177–189 (1977).

    Google Scholar 

  16. C. E.Rickart, General Theory of Banach Algebras. Princeton 1960.

  17. J. Zemánek, Spectral radius characterizations of commutativity in Banach algebras. StudiaMath.61, 257–268 (1977).

    Google Scholar 

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Srivastav, A. Commutativity criteria for real Banach algebras. Arch. Math 54, 65–72 (1990). https://doi.org/10.1007/BF01190670

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  • DOI: https://doi.org/10.1007/BF01190670

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