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Gleason–Kahane–Żelazko Theorem for Bilinear Maps


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[1] F.F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, New York, 1973.10.1007/978-3-642-65669-9 Search in Google Scholar

[2] A.M. Gleason, A characterization of maximal ideals, J. Analyse Math. 19 (1967), 171–172.10.1007/BF02788714 Search in Google Scholar

[3] N. Jacobson and C.E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), no. 3, 479–502. Search in Google Scholar

[4] K. Jarosz, Generalizations of the Gleason–Kahane–Żelazko theorem, Rocky Mountain J. Math. 21 (1991), no. 3, 915–921. Search in Google Scholar

[5] J.-P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339–343.10.4064/sm-29-3-339-343 Search in Google Scholar

[6] S.H. Kulkarni, Gleason–Kahane–Żelazko theorem for real Banach algebras, J. Math. Phys. Sci. 18 (1983/84), Special Issue, S19–S28. Search in Google Scholar

[7] T. Miura, S.-E. Takahasi, and G. Hirasawa, Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras, J. Inequal. Appl. 2005, no. 4, 435–441. Search in Google Scholar

[8] A.R. Sourour, The Gleason–Kahane–Żelazko theorem and its generalizations, in: J. Zemánek (ed.), Functional Analysis and Operator Theory, Banach Center Publ., 30, Polish Acad. Sci. Inst. Math., Warsaw, 1994, pp. 327–331.10.4064/-30-1-327-331 Search in Google Scholar

[9] E.C. Titchmarsh, The Theory of Functions, Reprint of the second (1939) edition, Oxford University Press, Oxford, 1976. Search in Google Scholar

[10] W. Żelazko, A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math. 30 (1968), 83–85.10.4064/sm-30-1-83-85 Search in Google Scholar

[11] A. Zivari-Kazempour, A characterisation of 3-Jordan homomorphisms on Banach algebras, Bull. Aust. Math. Soc. 93 (2016), no. 2, 301–306. Search in Google Scholar

[12] A. Zivari-Kazempour, Automatic continuity of n-Jordan homomorphisms on Banach algebras, Commun. Korean Math. Soc. 33 (2018), no. 1, 165–170. Search in Google Scholar

[13] A. Zivari-Kazempour, When is a bi-Jordan homomorphism bi-homomorphism?, Kragujevac J. Math. 42 (2018), no. 4, 485–493. Search in Google Scholar

[14] A. Zivari-Kazempour, Characterization of n-Jordan homomorphisms and their automatic continuity on Banach algebras, Ann. Univ. Ferrara (2022). DOI: 10.1007/s11565-022-00425-6 Open DOISearch in Google Scholar

eISSN:
2391-4238
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Mathematics, General Mathematics