학술저널
CAUCHY{RASSIAS STABILITY OF A GENERALIZED ADDITIVE MAPPING IN BANACH MODULES AND ISOMORPHISMS IN C¤{ALGEBRAS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 24, No. 4
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2011.11617 - 630 (14 pages)
- 2
then the odd mapping f : X ! Y is additive, and we prove the Cauchy-Rassias stability of the functional equation (z) in Banach modules over a unital C¤-algebra. As an application, we show that every almost linear bijection h : A ! B of a unital C¤-algebra A onto a unital C¤-algebra B is a C¤-algebra isomorphism when h(2nuy) = h(2nu)h(y) for all unitaries u 2 A, all y 2 A, and n = 0; 1; 2; ¢ ¢ ¢ .
1. Introduction
2. An odd functional equation in d variables
3. Stability of an odd functional equation in Banach modules over a C¤-algebra
4. Isomorphisms in unital C¤-algebras
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