MAPS PRESERVING m- ISOMETRIES ON HILBERT SPACE

Let H be a complex Hilbert space and B(H) the algebra of all bounded linear operators on H. In this paper, we prove that if phi : B(H) -> B(H) is a unital surjective bounded linear map, which preserves m- isometrics m = 1, 2 in both directions, then there are unitary operators U, V is an element of B(H) such that phi(T) = UTV or phi(T) = (UTV)-V-tr for all T is an element of B(H), where T-tr is the transpose of T with respect to an arbitrary but fixed orthonormal basis of H.