| 翟成波,梁展东.Hilbert投影距离与Banach空间的范数[J].数学研究及应用,2011,31(1):91~99 |
| Hilbert投影距离与Banach空间的范数 |
| Hilbert's Projective Metric and the Norm on a Banach Space |
| 投稿时间：2008-12-02 修订日期：2010-01-18 |
| DOI：10.3770/j.issn:1000-341X.2011.01.010 |
| 中文关键词: Hilbert投影距离 正规体锥 范数. |
| 英文关键词:Hilbert's projective metric normal and solid cone norm. |
| 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). |
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| 中文摘要: |
| 文给出了Hilbert投影距离与Banach空间范数之间的一些联系,结果表明在某类集合上Hilbert投影距离与范数的收敛性是等价的.作为主要结果的应用,讨论了一类正$\alpha$齐次算子的特征值问题和一类非线性代数系统的正解问题. |
| 英文摘要: |
| 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 $\alpha$ and the positive solutions for a class of nonlinear algebraic system. |
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