The Maximum Principle for Holomorphic Operator Functions

被引：3

作者：

Daniluk, Andrzej ^{[1
]}

机构：

[1] Jagiellonian Univ, Fac Math, Krakow, Poland

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2011年 / 69卷 / 03期

关键词：

Maximum principle; holomorphic operator function; Banach space; uniformly convex space; RESOLVENT NORM; LEVEL SETS; CONVEXITY;

D O I：

10.1007/s00020-010-1835-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if an operator-valued analytic function f of a complex variable attains its maximum modulus at z(0), then the coefficients of the nonconstant terms in the power series expansion about z(0) cannot be invertible, provided a complex uniform convexity condition holds. One application is that the norm of the resolvent of an operator on a complex uniformly convex space cannot have a local maximum.

引用

页码：365 / 372

页数：8

共 10 条

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