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| 自反Banach格上正算子基态的存在性 | |
| 引用本文： | 吕思江. 自反Banach格上正算子基态的存在性[J]. 纯粹数学与应用数学, 2008, 24(1): 136-139 |
| 作者姓名： | 吕思江 |
| 作者单位： | 中国科学技术大学统计与金融系,安徽,合肥,230026 |
| 摘 要： | 非负算子基态的存在性,是Perron-Frobenius型定理的核心内容,也是证明算子谱缝隙的主要步骤.本文主要利用了正算子非半紧测度的概念,讨论了一般自反Banach格上正算子基态的存在性,并得到了一个充分条件.更为特殊的,若算子同时满足不可约性,证明了基态特征向量是严格正的. |
| 关 键 词： | 正算子 基态 非半紧算子 非半紧测度 不可约算子 |
| 文章编号： | 1008-5513(2008)01-0136-04 |
| 修稿时间： | 2006-11-10 |
The existence of ground state for positive operators in reflective Banach lattices |
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| L Si-jiang. The existence of ground state for positive operators in reflective Banach lattices[J]. Pure and Applied Mathematics, 2008, 24(1): 136-139 | |
| Authors: | L Si-jiang |
| Affiliation: | L(U) Si-jiang |
| Abstract: | By making use of measure of non-semicompacmess,the author gives a sufficient condition for The existence of ground state for positive operators,which is considered crucial for the proof of spectral gap and theorem of Perron-Frobenius type.In addition,if the operator is irreducible,we could prove that the eigenvector is strict positive. |
| Keywords: | positive operators ground state measure of non-semicompactness irreducible operatos |
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