Hilbert's Projective Metric and the Norm on a Banach Space  

作　　者：Cheng Bo ZHAI Zhan Dong LIANG 

机构地区：[1]School of Mathematical Sciences, Shanxi University, Shanxi 030006, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第1期91-99,共9页数学研究与评论（英文版）

基　　金：Supported by the Natural Science Foundation of Shanxi Province (Grant No.20041003);the Youth Science Foundation of Shanxi Province (Grant No.2010021002-1)

摘　　要：In this paper, we establish some relations between the Hilbert＇s projective metric and the norm on a Banach space and show that the metric and the norm induce equivalent convergences at certain set. As applications, we utilize the main results to discuss the eigenvalue problems for a class of positive homogeneous operators of degree a and the positive solutions for a class of nonlinear algebraic system.In this paper, we establish some relations between the Hilbert＇s projective metric and the norm on a Banach space and show that the metric and the norm induce equivalent convergences at certain set. As applications, we utilize the main results to discuss the eigenvalue problems for a class of positive homogeneous operators of degree a and the positive solutions for a class of nonlinear algebraic system.

关 键 词：Hilbert＇s projective metric normal and solid cone norm. 

分 类 号：O177.91[理学—数学]