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Hilbert投影距离与Banach空间的范数
引用本文:翟成波,梁展东.Hilbert投影距离与Banach空间的范数[J].数学研究与评论,2011,31(1):91-99.
作者姓名:翟成波  梁展东
作者单位:山西大学数学科学学院, 山西 太原 030006;山西大学数学科学学院, 山西 太原 030006
基金项目:山西省自然科学基金(Grant No.20041003),山西省青年科学基金(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.

关 键 词:Hilbert's  projective  metric  normal  and  solid  cone  norm.
收稿时间:2008/12/2 0:00:00
修稿时间:2010/1/18 0:00:00

Hilbert's Projective Metric and the Norm on a Banach Space
Cheng Bo ZHAI and Zhan Dong LIANG.Hilbert''s Projective Metric and the Norm on a Banach Space[J].Journal of Mathematical Research and Exposition,2011,31(1):91-99.
Authors:Cheng Bo ZHAI and Zhan Dong LIANG
Institution:School of Mathematical Sciences,Shanxi University,Shanxi 030006,P.R.China
Abstract: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 $\alpha$ and the positive solutions for a class of nonlinear algebraic system.
Keywords:Hilbert's projective metric  normal and solid cone  norm  
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