Product of operators and the product of their numerical ranges
Chi-Kwong Li (李志光)教授 上午 10:30–12:00 Hongjing Hall 107 室Abstract:
We show that a compact operator A is a multiple of a positive operator if and only if the spectrum of AB is always a subset of the closure of the product of the numerical ranges W(A) and W(B) for any (rank one) operator B. The sufficiency may fail for a general operator A.