Abstract: Let H be a Hilbert space. B(H) denotes the Banach space of all bounded linear operators of H into H. Let T ={ f(z): f(z)=zI-∑^∞_n=2 zⁿA_n is analytic on the unit disk |z|<1, where the coefficients A_n are compact positive Hermitian operators of H into H and I denotes the identity operator on H, ∑^∞_n=2 n(A_n x, x) ≤ 1 for any x ∈ H with ∣|x|∣=1. In this paper the author investigates the extreme points of T .

Key words: Extreme point, Compact positive Hermitian operator, Hermitian matrix