NUMERICAL RADIUS INEQUALITIES FOR OPERATOR MATRICES

Several numerical radius inequalities for operator matrices are proved by generalizing earlier inequalities. In particular, the following inequalities are obtained: if n is even, 2w(T) <= max{parallel to A(1)parallel to,parallel to A(2)parallel to,. . . , parallel to A(n)parallel to} + 1/2 Sigma(n-1)(k=0)parallel to vertical bar A(n-k)vertical bar(t)vertical bar A(k+1)*vertical bar(1-t)parallel to, and if n is odd, 2w(T) <= max{parallel to A(1)parallel to,parallel to A(2)parallel to, . . . ,parallel to A(n)parallel to}+w((A) over tilde ((n+1/2)t))+1/2 Sigma(n-1)(k=0)parallel to vertical bar A(n-k)vertical bar(t)vertical bar A(k+1)*vertical bar(1-t)vertical bar, for all t is an element of [0, 1], A(i)'s are bounded linear operators on the Hilbert space H, and T is off diagonal matrix with entries A(1), . . . , A(n).