摘要
发展了 Ky Fan[1] 中定理 4的结果 ,对复的 Hilbert空间 H上的真压缩算子 A和单位圆盘△内的解析函数 f 给出了优势原理 .与文 [5]比较 ,本文去掉 A为正规算子的限制 ,并改进了相应的结果 .对 H (△ )的某个子类中的 f ,给出‖ f′( A)‖的估值 .并讨论了从属关系的优势原理 ,特别是把 Shah- Goluzin关于从属于单叶函数的优势半径
This paper extends the results of theorem 4 in Ky Fan\+\{[1]\}. For proper contraction operator A defined in the complex Hibert space H and analytic function f defined in the unit disk △ the majorization principle is established. Compared with [5], in this paper the condition which A is normal operator is canceled and, the corresponding results are improved. Further, for functions f which belong to some subclass of H(△) , the value of ‖f′(A)‖ is estimated. Moreover, the majorization principle of subordinate relation also is discussed and, the superior radius criteria\+\{[7]\} of univalent functions given by Shah Goluzin are extended to operator functions.
