Superstability of homomorphisms and derivations on C*-algebras: A fixed point approach
Let A be a unital C*-algebras. B be a Bausch algebra and let X be a Banach A-module. By using fixed pint methods, we prove that: i) Every almost linear mapping h : A -> B which satisfies h(2(n)uy) = h(2(n)u)h(y) for all U is an element of A(+), all y is an element of A, and all n = 0,1, 2, ..., is a homomorphism. ii) Every almost linear continuous mapping d : A -> X is a derivation when d(2(n)uy) = d(2(n)u)y + 2(n)ud(y) holds for all u is an element of A(+), all Y is an element of A, and all n = 0, 1, 2,....
homomorphism derivation alternative fixed point