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 inter...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.展开更多
基金Supported by the National Natural Science Foundation of China(No.10871144)the Natural Science Foundation of Tianjin(No.07JCYBJC05200)
文摘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.
