Hilbert's Projective Metric and the Norm on a Banach Space
Received:December 02, 2008  Revised:January 18, 2010
Key Word: Hilbert's projective metric   normal and solid cone   norm.  
Fund ProjectL:Supported by the Natural Science Foundation of Shanxi Province (Grant No.20041003) and the Youth Science Foundation of Shanxi Province (Grant No.2010021002-1).
Author NameAffiliation
Cheng Bo ZHAI School of Mathematical Sciences, Shanxi University, Shanxi 030006, P. R. China 
Zhan Dong LIANG School of Mathematical Sciences, Shanxi University, Shanxi 030006, P. R. China 
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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.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.01.010
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