Let X, Y be Banach modules over a C*-algebra and let r, s be positive real numbers. We prove the stability of the following functional equation in Banach modules over a unital C*- algebra: rf (s(x - y)) + sf (r(y - x)) + (r + s)f (rx + sy) = (r + s) (rf(x) + sf(y)) . (0.1) We show that if r = s and an odd mapping f : X → Y satisfies the functional equation (0.1) then the odd mapping f : X → Y is Cauchy additive. 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((2r)duy) = h((2r)du)h(y) for all unitaries u ∈ A, all y ∈ A, and all d ∈ Z.
|Number of pages||14|
|Journal||International Journal of Applied Mathematics and Statistics|
|State||Published - 2007 Feb 1|
- Euler-Lagrange type additive mapping
- Hyers-Ulam stability
- Isomorphism between C*-algebras