摘要
1.引言 设H为复Hilbert空间,L(H)表示H上所有连续线性算子组成的Banach空间。若f(z)为定义在复平面区域D上的算子值函数,f(z)∈L(H)(z∈D),我们称f(z)于D上解析,是指对L(H)上的每个连续线性泛函φ,φ(f(z))为D上通常的复值解析函数,其全体记为A_H(D)。
Let L( H ) be the complex Banach space of all continous linear, operators on Hilbert space H and AH(D) denote all. analytic operator functions defined on domain D in the complex plane with values in L(H).Set We obtain a result with method of function theory which may deduce the main theorem in [1 ]. . Theorem.Let . Let Then there exists a sequence of functions f(k)(z) that belong to and satisfy the following;( 1 ) ;(2) and( 3 ) has a zero of at least order
