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Continuity of derivations on some semiprime Banach algebra


Author: Ramesh V. Garimella
Journal: Proc. Amer. Math. Soc. 99 (1987), 289-292
MSC: Primary 46J05
DOI: https://doi.org/10.1090/S0002-9939-1987-0870787-6
MathSciNet review: 870787
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Abstract: If every prime ideal is closed in a commutative semiprime Banach algebra with unit, then every derivation on it is continuous. Also if derivations are continuous on integral domains, then they are continuous on semiprime Banach algebras.


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  • [1] W. G. Bade and P. C. Curtis, Jr., Prime ideals and automatic continuity for Banach algebras, J. Funct. Anal. 29 (1978), 88-103. MR 499936 (80j:46077)
  • [2] Philip C. Curtis, Jr., Derivations on commutative Banach algebras (Proc., Long Beach, 1981), Lecture Notes in Math., vol. 975, Springer-Verlag, pp. 328-333. MR 697597 (84f:46075)
  • [3] J. Cusack, Automatic continuity and topologically simple radical Banach algebras, J. London Math. Soc. 21 (1977), 493-500. MR 0461136 (57:1121)
  • [4] J. Esterle, Elements for a classification of commutative radical Banach algebras (Proc, Long Beach, 1981), Lecture Notes in Math., vol. 975, Springer-Verlag, pp. 4-65. MR 697578 (84h:46064)
  • [5] S. Grabiner, The nilpotency of Banach nil algebras, Proc. Amer. Math. Soc. 21 (1969), 510. MR 0236700 (38:4995)
  • [6] -, A formal power series operational calculus for quasinipotent operators. II, J. Math. Anal. Appl. 43 (1973), 170-192. MR 0358410 (50:10876)
  • [7] B. E. Johnson, Continuity of derivations on commutative algebras,, Amer. J. Math. 91 (1969), 1-10. MR 0246127 (39:7433)
  • [8] A. Khosravi, Derivations on commutative Banach algebras, Proc. Amer. Math. Soc. 84 (1982), 60-64. MR 633278 (83b:46066)
  • [9] M. Singer and J. Wermer, Derivatives on commutative normed algebras, Math. Ann. 129 (1955), 260-264. MR 0070061 (16:1125c)

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DOI: https://doi.org/10.1090/S0002-9939-1987-0870787-6
Article copyright: © Copyright 1987 American Mathematical Society

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