SOME GENERALIZATIONS OF NUMERICAL RADIUS ON OFF-DIAGONAL PART OF 2 x 2 OPERATOR MATRICES

We generalize several inequalities involving powers of the numerical radius for off- diagonal part of 2 x 2 operator matrices of the form T =[(0)(B)(C)(0)], where B,C are two operators. In particular,if T = [(0)(B)(C)(0)],then we get 1/2(3/2()(r)(-1))max {parallel to mu parallel to,parallel to eta parallel to} <= w(r) (T) <= 1/2(r)(+1)max {parallel to mu parallel to,parallel to eta parallel to}, where r >= 2, mu = vertical bar (C - B*)-i(C + B*)+ i(C + B*)vertical bar(r)and eta = vertical bar(B -C*) + i(B + C*)(r)+ vertical bar (C*- B)+ i(B + C*)(r).