COMMUTATIVITY PRESERVINE MAPS ON OPERATOR ALGEBRAS

Let H and K are Hilbert space, B (H) and B(K) denote the algebras of all bounded linear operators on H and K, respectively and B+(H) be of all positive operator on H. It is shown that if φ be a linear map from B(H) into B(K) satisfies 1) φ(x2) φ(x)= φ(x) φ(x2), x Є B+(h), then φ perserves commutativity when one of the elements is normal.

کلیدواژه ها:

Operator algebra ، Commutativity preserving map