MEAN VALUE OF ANALYTIC OPERATOR FUNCTIONS

数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (4): 468-473.

MEAN VALUE OF ANALYTIC OPERATOR FUNCTIONS

喻小培¹, 蹇明²

1. Dept. of Math., Central China Normal University, Wuhan 430070, China;
2. Dept. of Math. & Physics, Wuhan Univ. of Technology, Wuhan 430070, China

收稿日期:1992-11-15 修回日期:1994-10-15 出版日期:1995-12-25 发布日期:1995-12-25

MEAN VALUE OF ANALYTIC OPERATOR FUNCTIONS

Yu Xiaopei¹, Jian Ming²

1. Dept. of Math., Central China Normal University, Wuhan 430070, China;
2. Dept. of Math. & Physics, Wuhan Univ. of Technology, Wuhan 430070, China

Received:1992-11-15 Revised:1994-10-15 Online:1995-12-25 Published:1995-12-25

摘要/Abstract

摘要： In this paper,it is proved that if A is a normal proper contraction on Hilbert space H and F(z)=U(z)+iV(z) is operator-valued analytic on the unit disc △ and 0 < p < 1,then||F(A)||^p ≤ ||F(0)||^p+C_p(1-||A||)^-2× sup_{0 < t < 1}∬_△||U[(At-εI)(I-εA·t)^-1]||^pdm(ε).

关键词: Hilbert space, operator, operator-valued function, proper contraction

Abstract: In this paper,it is proved that if A is a normal proper contraction on Hilbert space H and F(z)=U(z)+iV(z) is operator-valued analytic on the unit disc △ and 0 < p < 1,then||F(A)||^p ≤ ||F(0)||^p+C_p(1-||A||)^-2× sup_{0 < t < 1}∬_△||U[(At-εI)(I-εA·t)^-1]||^pdm(ε).

Key words: Hilbert space, operator, operator-valued function, proper contraction

喻小培, 蹇明. MEAN VALUE OF ANALYTIC OPERATOR FUNCTIONS[J]. 数学物理学报(英文版), 1995, 15(4): 468-473.

Yu Xiaopei, Jian Ming. MEAN VALUE OF ANALYTIC OPERATOR FUNCTIONS[J]. Acta mathematica scientia,Series B, 1995, 15(4): 468-473.

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MEAN VALUE OF ANALYTIC OPERATOR FUNCTIONS

MEAN VALUE OF ANALYTIC OPERATOR FUNCTIONS

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