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1996 | 118 | 3 | 205-229
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Derivations on Jordan-Banach algebras

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We establish that all derivations on a semisimple Jordan-Banach algebra are automatically continuous. By showing that "almost all" primitive ideals in the algebra are invariant under a given derivation, the general case is reduced to that of primitive Jordan-Banach algebras.
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  • [1] B. Aupetit, The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras, J. Funct. Anal. 47 (1982), 1-6.
  • [2] M. Cabrera, A. Moreno and A. Rodríguez, Zel'manov's theorem for primitive Jordan-Banach algebras, J. London Math. Soc., to appear.
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  • [7] B. E. Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73 (1967), 537-539.
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  • [9] B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, ibid. 90 (1968), 1067-1073.
  • [10] K. B. Laursen, Some remarks on automatic continuity, in: Lecture Notes in Math. 512, Springer, 1976, 96-108.
  • [11] K. McCrimmon, The radical of a Jordan algebra, Proc. Nat. Acad. Sci. U.S.A. 59 (1969), 671-678.
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  • [13] A. Rodríguez, The uniqueness of the complete norm topology in complete normed nonassociative algebras, J. Funct. Anal. 60 (1985), 1-15.
  • [14] A. Rodríguez, An approach to Jordan-Banach algebras from the theory of nonassociative complete normed algebras, Ann. Sci. Univ. Clermont-Ferrand II Math. 27 (1991), 1-57.
  • [15] A. Rodríguez, Jordan structures in analysis, in: Jordan Algebras, Proc. Conf. Oberwolfach, August 9-15, 1992, W. Kaup, K. McCrimmon and H. Petersson (eds.), de Gruyter, Berlin, 1994, 97-186.
  • [16] A. M. Sinclair, Jordan homomorphisms and derivations on semisimple Banach algebras, Proc. Amer. Math. Soc. 24 (1970), 209-214.
  • [17] A. M. Sinclair, Continuity of Linear Operators, London Math. Soc. Lecture Note Ser. 21, Cambridge University Press, 1976.
  • [18] M. P. Thomas, Primitive ideals and derivations on non-commutative Banach algebras, Pacific J. Math. 159 (1993), 139-152.
  • [19] A. R. Villena, Continuity of derivations on a complete normed alternative algebra, J. Inst. Math. Comput. Sci. 3 (1990), 99-106.
  • [20] A. R. Villena, Continuity of derivations on H*-algebras, Proc. Amer. Math. Soc. 122 (1994), 821-826.
  • [21] E. I. Zel'manov, On prime Jordan algebras, Algebra i Logika 18 (1979), 162-175 (in Russian).
  • [22] E. I. Zel'manov, On prime Jordan algebras II, Siberian Math. J. 24 (1983), 89-104.
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