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A Generalization of the Gleason–Kahane–Zelazko Theorem to Topological Vector Spaces

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Abstract

In this paper, we give a version of the Gleason–Kahane–Zelazko theorem for continuous linear functionals on some topological algebras and topological vector spaces of functions.

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References

  1. Arens, R.: The space \(L^\omega \) and convex topological rings. Bull. Am. Math. Soc. 52, 931–935 (1946)

    Article  MathSciNet  Google Scholar 

  2. Bhatt, S.J.: On Arense’ algebra \(L^\omega \). Glas. Math. 15(35), 305–314 (1980)

    Google Scholar 

  3. Bhatt, S.J.: On Arense’ algebra \(L^\omega \) \(II\). Glas. Math. 16(36), 297–306 (1981)

    Google Scholar 

  4. Fricain, E., Mashreghi, J.: The Theory of \(H(b)\) Spaces, vol. I and II. Cambridge University Press, Cambridge (2015)

    MATH  Google Scholar 

  5. Gleason, A.M.: A characterization of maximal ideals. J. Anal. Math. 19, 171–172 (1967)

    Article  MathSciNet  Google Scholar 

  6. Husain, T.: Multiplicative Functionals on Topological Algebras, Research Notes in Mathematics, vol. 85. Pitman Books Limited, Boston (1983)

  7. Kahane, J.P., Zelazko, W.: A characterization of maximal ideals in commutative Banach algebras. Studia Math. 29, 339–343 (1968)

    Article  MathSciNet  Google Scholar 

  8. Mashreghi, J., Ransford, T.: A Gleason–Kahane–Zelazko theorem for modules and applications to holomorphic function spaces. Bull. Lond. Math. Soc. 47(6), 1014–1020 (2015)

    Article  MathSciNet  Google Scholar 

  9. Zelazko, W.: A characterization of multiplicative linear functionals in complex Banach algebras. Studia Math. 30, 83–85 (1968)

    Article  MathSciNet  Google Scholar 

  10. Zhu, K.: Operator Theory in Function Spaces, 2nd edn. American Mathematical Society, Providence (2007)

    Book  Google Scholar 

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Correspondence to A. Golbaharan.

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Golbaharan, A. A Generalization of the Gleason–Kahane–Zelazko Theorem to Topological Vector Spaces. Mediterr. J. Math. 17, 69 (2020). https://doi.org/10.1007/s00009-020-1499-3

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  • DOI: https://doi.org/10.1007/s00009-020-1499-3

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