RANGE-PRESERVING MAPS ON OPERATOR ALGEBRAS

Let X,Y and Z are Banach Spaces, B(X,Z) denote the algebras of all bounded linear operators from X into C(X) be all of continuos complex valued function on X. we show that if φ be a map from B(X,Z) into B(Y,Z) satisfies (u ο f) φ (T)(Y) = uT(X) for every TЄB (X,Z), uЄc(X) and for some continuous function f from Y into X, then φ by choosing f=I we conclude that φ is identity.

کلیدواژه ها:

Operator algebra ، range preserving map