Operator-valued typically real functions induced by a contraction

Let H be a complex Hilbert space and let L(H) denote the algebra of all bou nded linear operators on H. Let F(z) = Sigma(n=0)(infinity) z(n) A(n) be an operator-valued analytic function whose coefficients are bounded operators in L(H) for z in the open unit disc D and the series is convergent in the strong operator topology. In this paper, we discuss operator-valued typical ly real functions F(z) = Sigma(n=0)(infinity) z(n) A(n) which generalize co mplex-valued typically real functions. We characterize operator-valued typi cally real functions and study such functions F(z) induced by a contraction on H. In addition, we consider m x n-tuple operator-valued typically real functions and positively real functions. Finally, we charaterize operator-v alued typically rear functions in the finite-dimensional cases. (C) 1999 Ac ademic Press.