UPPER BOUNDS FOR NUMERICAL RADIUS INEQUALITIES INVOLVING OFF-DIAGONAL OPERATOR MATRICES

In this article, we establish some upper bounds for numerical radius inequalities, including those of 2 x 2 operator matrices and their offdiagonal parts. Among other inequalities, it is shown that if T = [(Y 0) (0 X)], then omega(r)(T) <= 2(r-2) parallel to f(2r) (vertical bar X vertical bar) + g(2r) (vertical bar Y*vertical bar)parallel to(1/2)parallel to f(2r) (vertical bar Y vertical bar) + g(2r) (vertical bar X*vertical bar)parallel to(1/2) and omega(r) (T) <= 2(r-2) parallel to f(2r) (vertical bar X vertical bar) + f(2r) (vertical bar Y*vertical bar)parallel to(1/2)parallel to g(2r) (vertical bar Y vertical bar) + g(2r) (vertical bar X*vertical bar)parallel to(1/2), where X, Y are bounded linear operators on a Hilbert space H, r >= 1, and f, g are nonnegative continuous functions on [0, infinity) satisfying the relation f(t)g(t) = t (t is an element of [0, infinity)). Moreover, we present some inequalities involving the generalized Euclidean operator radius of operators T-1 . . . T-n.