Browse > Article
http://dx.doi.org/10.5831/HMJ.2012.34.1.55

STABILITY FOR JORDAN LEFT DERIVATIONS MAPPING INTO THE RADICAL OF BANACH ALGEBRAS  

Park, Won-Gil (Department of Mathematics Education, Mokwon University)
Chang, Ick-Soon (Department of Mathematics, Mokwon University)
Publication Information
Honam Mathematical Journal / v.34, no.1, 2012 , pp. 55-62 More about this Journal
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
Jordan left derivation; Left derivation; Banach algebra; Stability;
Citations & Related Records
연도 인용수 순위
  • Reference
1 D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27 (1941), 222-224.   DOI   ScienceOn
2 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approxi- mately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436.   DOI   ScienceOn
3 G. Isac, Th.M. Rassias, On the Hyers-Ulam stability of $\psi$-additive mappings, J. Approx. Theory, 72 (1993), 131-137.   DOI   ScienceOn
4 B.E. Johnson, Continuity of derivations on commutative Banach algebras, Amer. J. Math., 91 (1969), 1-10.   DOI   ScienceOn
5 T. Miura, G. Hirasawa and S.-E. Takahasi, A pertubation of ring derivations on Banach algebras, J. Math. Anal. Appl., 319 (2006), 522-530.   DOI   ScienceOn
6 Y.H. Lee and K.W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc., 128 (1999), 1361-1369.   DOI   ScienceOn
7 M.S. Moslehian, Hyers-Ulam-Rassias stability of generalized derivations, Int. J. Math. Math. Sci., (2006), Art. ID 93942, 8 pp.
8 C. Park, Linear derivations on Banach algebras, Nonlinear. Funct. Anal. Appl., 9 (2004), 359-368.
9 Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.   DOI   ScienceOn
10 P. Semrl, The functional equation of multiplicative derivation is superstable on standard operator algebras, Integr. Equat. Oper. Theory 18 (1994), 118-122.   DOI
11 I.M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann, 129 (1955), 260-264.   DOI
12 M.P. Thomas, The image of a derivation is contained in the radical, Ann. of Math., 128 (1988), 435-460.   DOI
13 S.M. Ulam, Problems in Modern Mathematics, Chap. VI, Science ed., Wiley, New York., (1960).
14 T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc., Japan 2 (1950), 64-66.   DOI
15 D.G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397.   DOI
16 R. Badora, On approximate ring homomorphisms, J. Math. Anal. Appl. 276 (2002), 589-597.   DOI   ScienceOn
17 R. Badora, On approximate derivations, Math. Inequal. Appl. 9 (2006), 167-173.
18 F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, New York, Heidelberg and Berlin, (1973).
19 M. Bresar and J. Vukman, On the left derivation and related mappings, Proc. Amer. Math. Soc., 10 (1990), 7-16.
20 D. Han and F. Wei, Generalized Jordan left derivations on semiprime algebras, Monatsh. Math. Soc., 161 (2010), 77-83.   DOI
21 O. Hatori and J. Wada, Ring derivations on semi-simple commutative Banach algebras, Tokyo J. Math., 15 (1992), 223-229.   DOI