On reduced minimum modulus preservers

Suppose ( ) denotes the reduced minimum modulus in a Banach algebra. We show thata continuous surjective linear map from a unital Banach algebra A onto a C -algebra Bsatisfying (φ(a)φ(b)) = (ab) (a; b ۲ A); makes A to be a C -algebra -isomorphic to B upto multiplication by a central invertible element. If B(H) is the C -algebra of all boundedlinear operators on a Hilbert space H, we characterize surjective maps φ on B(H) (with nolinearity and continuity assumption) preserving the reduced minimum modulus of operatorproducts.

Keywords:

reduced minimum modulus , preserver maps , operators on a Hilbert space