Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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STABILITY FOR JORDAN LEFT DERIVATIONS MAPPING INTO THE RADICAL OF BANACH ALGEBRAS

  • Received : 2011.11.15
  • Accepted : 2011.12.19
  • Published : 2012.03.25
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Abstract

In this article, we take account of stability for ring Jordan left derivations and ring left derivations and we also deal with problems for the radical ranges of linear Jordan left derivations and linear left derivations.

Keywords

References

  1. T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc., Japan 2 (1950), 64-66. https://doi.org/10.2969/jmsj/00210064
  2. R. Badora, On approximate ring homomorphisms, J. Math. Anal. Appl. 276 (2002), 589-597. https://doi.org/10.1016/S0022-247X(02)00293-7
  3. R. Badora, On approximate derivations, Math. Inequal. Appl. 9 (2006), 167-173.
  4. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, New York, Heidelberg and Berlin, (1973).
  5. D.G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397. https://doi.org/10.1215/S0012-7094-49-01639-7
  6. M. Bresar and J. Vukman, On the left derivation and related mappings, Proc. Amer. Math. Soc., 10 (1990), 7-16.
  7. D. Han and F. Wei, Generalized Jordan left derivations on semiprime algebras, Monatsh. Math. Soc., 161 (2010), 77-83. https://doi.org/10.1007/s00605-009-0116-0
  8. O. Hatori and J. Wada, Ring derivations on semi-simple commutative Banach algebras, Tokyo J. Math., 15 (1992), 223-229. https://doi.org/10.3836/tjm/1270130262
  9. D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  10. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approxi- mately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
  11. G. Isac, Th.M. Rassias, On the Hyers-Ulam stability of $\psi$-additive mappings, J. Approx. Theory, 72 (1993), 131-137. https://doi.org/10.1006/jath.1993.1010
  12. B.E. Johnson, Continuity of derivations on commutative Banach algebras, Amer. J. Math., 91 (1969), 1-10. https://doi.org/10.2307/2373262
  13. T. Miura, G. Hirasawa and S.-E. Takahasi, A pertubation of ring derivations on Banach algebras, J. Math. Anal. Appl., 319 (2006), 522-530. https://doi.org/10.1016/j.jmaa.2005.06.060
  14. Y.H. Lee and K.W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc., 128 (1999), 1361-1369. https://doi.org/10.1090/S0002-9939-99-05156-4
  15. M.S. Moslehian, Hyers-Ulam-Rassias stability of generalized derivations, Int. J. Math. Math. Sci., (2006), Art. ID 93942, 8 pp.
  16. C. Park, Linear derivations on Banach algebras, Nonlinear. Funct. Anal. Appl., 9 (2004), 359-368.
  17. Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  18. P. Semrl, The functional equation of multiplicative derivation is superstable on standard operator algebras, Integr. Equat. Oper. Theory 18 (1994), 118-122. https://doi.org/10.1007/BF01225216
  19. I.M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann, 129 (1955), 260-264. https://doi.org/10.1007/BF01362370
  20. M.P. Thomas, The image of a derivation is contained in the radical, Ann. of Math., 128 (1988), 435-460. https://doi.org/10.2307/1971432
  21. S.M. Ulam, Problems in Modern Mathematics, Chap. VI, Science ed., Wiley, New York., (1960).