CAUCHY-RASSIAS STABILITY OF LINEAR MAPPINGS IN BANACH MODULES ASSOCIATED WITH A GENERALIZED JENSEN TYPE MAPPING
- Authors
- Park, Choonkil; Song, Jung Hwan
- Issue Date
- Nov-2009
- Publisher
- SPRINGER SINGAPORE PTE LTD
- Keywords
- Cauchy-Rassias stability; C*-algebra homomorphism; Poisson C*-algebra homomorphism; Poisson Banach module over Poisson C*-algebra; Poisson JC*-algebra homomorphism
- Citation
- BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, v.35, no.2, pp.143 - 162
- Indexed
- SCIE
SCOPUS
- Journal Title
- BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
- Volume
- 35
- Number
- 2
- Start Page
- 143
- End Page
- 162
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/175956
- ISSN
- 1017-060X
- Abstract
- Let X and Y be vector spaces. We show that a mapping f : X -> Y satisfies the functional equation, f (x(1) + Sigma(2d)(j=2)(-1)(j)x(j))-f (x(1) + Sigma(2d)(j=2)(-1)(j-1)x(j)) = 2 Sigma(2d)(j=2)(-1)(j) f(x(j)) j= 2 (- 1) j f( xj) if and only if the mapping f : X -> Y is Cauchy additive, and prove the Cauchy-Rassias stability of the above functional equation in Banach modules over a unital C*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C*-algebras, Poisson C*-algebras or Poisson JC*-algebras. As an application, we show that every almost homomorphism h : A -> B of A into B is a homomorphism when h(2(n) uy) = h(2(n)u) h(y) or h(2(n)u circle y) = h(2(n) u) circle h(y), for all unitaries u is an element of A, all y is an element of A, and n = 0, 1, 2, ... . Moreover, we prove the Cauchy-Rassias stability of homomorphisms in C*-algebras, Poisson C*-algebras or Poisson JC*-algebras.
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