摘要
本文讨论Hilbert空间上一类三阶二元算子方程组给出所有重交换的解(A,C).作为应用,得到算子张量积A(?)B+C(?)D和A_1(?)A_2(?)…(?)A.为拟正规算子的充分必要条件.
In this paper we give all doubly commuting solutions to the simultaneous operator equations A* AC = a A~*A^2 + βAA*A and AA*C = λA* A^2 + γAA*A on a Hilbert space with operators A and C unknown. And, as an application, we find the necessary and sufficient conditions for a tensor product A(?)B + C(?) of operators to be quasinormal.
基金
Supported by the Provincial Natural Science Foundation of Shanxi
