一类算子值解析函数族的极值点

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

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-sum from n=2 to∞z^n A_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,sum from n=2 to∞n(A_nx,x)≤1对所有x∈H,‖x‖=1成立}.该文研究了函数族T的极值点.

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 z^n An is analytic on the unit disk ｜z｜ 〈 1, where the coefficients As are compact positive Hermitian operators of H into H and Idenotes the identity operator on H, ∞∑ n=2 n（Anx,x） ≤ for any x ∈ H with ‖x‖. In this paper the author investigates the extreme points of T.