Numerical Range of Lie Product of Operators

作者：Hou, Jinchuan; Li, Chi-Kwong; Qi, Xiaofei^*

来源：Integral Equations and Operator Theory, 2015, 83(4): 497-516.

DOI：10.1007/s00020-015-2261-2

• Numerical ranges
• Lie products
• Hilbert spaces
• Preservers

Denote by W(A) the numerical range of a bounded linear operator A, and the Lie product of two operators A and B. Let H,K be complex Hilbert spaces of dimension and be a map whose range contains all operators of rank . It is shown that satisfies that for any if and only if dim H = dim K, there exist , a functional , a unitary operator , and a set of operators in , that consists of operators of the form aP + bI for an orthogonal projection P on H if the dimension of H is at least 3, such that where is the transpose of A with respect to an orthonormal basis of H. The proof of this result depends on the classifications of operators A or operator pairs A, B with some symmetric properties of W([A, B]) that are of independent interest.

• 出版日期2015-12
• 单位太原理工大学; 山西大学