JORDAN MAPS AND PSEUDOSPECTRUM IN C*-ALGEBRAS

We show that a surjective map q between two unital C*-algebras A and B, with phi(0) = 0, satisfies Lambda(epsilon)(phi(x(1)) - phi(x(2))) = Lambda(epsilon)(x(1) - x(2)), (x(1), x(2) is an element of A), where Lambda(epsilon) denotes the epsilon-pseudospectrum, if and only if phi is a Jordan *-isomorphism. We also characterize maps phi(1) and phi(2) from A onto B that satisfy Lambda(epsilon)(phi(1)(x(1)) - phi(2)(x(2))) = Lambda(epsilon)(x(1)x(2)), (x(1), x(2) is an element of A), or some other binary operations, in terms of Jordan *-isomorphisms. The main results imply several other characterizations of Jordan *-isomorphisms which are interesting in their own right.