一类算子值解析函数族的极值点

设 H 是一个Hilbert空间. B(H) 表示所有H 到 H 的有界线性算子构成的Banach空间. 设 T= {f(z): f(z)=zI-∑^∞_n=2 zⁿA_n 在单位圆盘|z|<1上解析, 其中系数A_n是 H 到 H 的紧正Hermitian算子, I 表示 H 上的恒等算子, ∑^∞_n=2 n(A_n x, x) ≤1 对所有x ∈H, ∣|x∣∣=1 成立. 该文研究了函数族 T 的极值点.

The Extreme Points of a Class of Analytic Operator-valued Functions

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 .