A perturbation of ring derivations on Banach algebras |
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| Authors: | Takeshi Miura Go Hirasawa |
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| Affiliation: | a Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 992-8510, Japan
b Department of Mathematics, Nippon Institute of Technology, Miyashiro, Saitama 345-8501, Japan |
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| Abstract: | Suppose A is a Banach algebra and suppose  is an approximate ring derivation in the sense of Hyers-Ulam-Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300]. If A has an approximate identity, or if A is semisimple and commutative, then we prove that f is an exact ring derivation. |
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| Keywords: | Ring derivation Hyers-Ulam-Rassias stability |
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