Some ω-unique and ω-ΡProperties for Linear Transformations on Hilbert Spaces  

作　　者：Xin-he Miao Zheng-hai Huang Ji-ye Han 

机构地区：[1]Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China [2]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Acta Mathematicae Applicatae Sinica》2010年第1期23-32,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10871144);the Natural Science Foundation of Tianjin(No.07JCYBJC05200)

摘　　要：Given a real （finite-dimensional or infinite-dimensional） Hilbert space H with a Jordan product, we introduce the concepts of ω-unique and ω-P properties for linear transformations on H, and investigate some interconnections among these concepts. In particular, we discuss the ω-unique and ω-P properties for Lyapunov-like transformations on H. The properties of the Jordan product and the Lorentz cone in the Hilbert space play important roles in our analysis.Given a real （finite-dimensional or infinite-dimensional） Hilbert space H with a Jordan product, we introduce the concepts of ω-unique and ω-P properties for linear transformations on H, and investigate some interconnections among these concepts. In particular, we discuss the ω-unique and ω-P properties for Lyapunov-like transformations on H. The properties of the Jordan product and the Lorentz cone in the Hilbert space play important roles in our analysis.

关 键 词：Linear complementarity problem Jordan product Lorentz cone ω-P property column sufficient property ω-uniqueness property 

分 类 号：O177.1[理学—数学] TD325[理学—基础数学]