Jul, 2006
A perturbation of ring derivations on Banach algebras
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- ,
- ,
- Volume
- 319
- Number
- 2
- First page
- 522
- Last page
- 530
- Language
- English
- Publishing type
- Research paper (scientific journal)
- DOI
- 10.1016/j.jmaa.2005.06.060
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
Suppose A is a Banach algebra and suppose f : A -> A 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. (c) 2005 Elsevier Inc. All rights reserved.
- Link information
- ID information
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- DOI : 10.1016/j.jmaa.2005.06.060
- ISSN : 0022-247X
- Web of Science ID : WOS:000240390700011