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http://dx.doi.org/10.14403/jcms.2011.24.3.14

APPROXIMATELY CENTRALIZING DERIVATIONS OF NONCOMMUTATIVE BANACH ALGEBRA  

Chang, Ick-Soon (Department of Mathematics Mokwon University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.24, no.3, 2011 , pp. 543-551 More about this Journal
Abstract
In this paper, we consider the functional inequalities with approximately centralizing derivations on noncommutative Banach algebras, and investigate the problem that functions satisfying the functional inequalities mentioned above map into the radical.
Keywords
functional inequality; derivation; stability; noncommutative Banach algebra; Jacobson radical;
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1 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.   DOI   ScienceOn
2 P. Semrl, The functional equation of multiplicative derivation is superstable on standard operator algebras, Integr. Equat. Oper. Theory 18 (1994), 118-122.   DOI   ScienceOn
3 I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260-264.   DOI   ScienceOn
4 M. P. Thomas, The image of a derivation is contained in the radical, Ann. of Math. 128 (1988), 435-460.   DOI   ScienceOn
5 S. M. Ulam, A Collection of Mathematical Problems, Interscience Publ., New York, 1960.
6 T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66.   DOI
7 R. Badora, On approximate ring homomorphisms, J. Math. Anal. Appl. 276 (2002), 589-597.   DOI   ScienceOn
8 R. Badora, On approximate derivations, Math. Inequal. Appl. 9 (2006), 167-173.
9 H. E. Bell and W. S. Martindale III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987), 92-101.   DOI
10 D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397.   DOI
11 M. Bresar, Centralizing mappings on von Neumann algebras, Proc. Amer. Math. Soc. 111 (1991), 501-510.   DOI
12 O. Hatori and J. Wada, Ring derivations on semi-simple commutative Banach algebras, Tokyo J. Math. 15 (1992), 223-229.   DOI
13 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224.   DOI   ScienceOn
14 B. E. Johnson, Continuity of derivations on commutative Banach algebras, Amer. J. Math. 91 (1969), 1-10.   DOI   ScienceOn
15 M. Mathieu and G.J. Murphy, Derivations mapping into the radical, Arch. Math. (Basel) 57 (1991), 469-474.   DOI   ScienceOn
16 T. Miura, G. Hirasawa and S.-E. Takahasi, A perturbation of ring derivations on Banach algebras, J. Math. Anal. Appl. 319 (2006), 522-530.   DOI   ScienceOn