Matrix Order in Bohr Inequality for Operators (Report‪)‬

1. INTRODUCTION Let H be a complex separable Hilbert space and B(H) the algebra of all bounded operators on H. We say that A [member of] B(H) is a positive operator if (Ax, x) [greater than or equal to] 0 for all x [member of] H, denoted by A [greater than or equal to] 0. The absolute value of A [member of] B(H) is denoted by [absolute value of A] = [([A.sup.*] A).sup.1/2].