算子方程的解及算子张量积

Solution of Opertor Equations and Tensor products

中文摘要:

      本文讨论Hilbert空间上一类三阶二元算子方程组A^*AC = αA^*A² + βAA^*A;AA^*C = λA^*A² + γAA^*A,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A₁(?)A₂(?)…(?)A_n为拟正规算子的充分必要条件.

英文摘要:

      In this paper we give all doubly commuting solutions to the simultaneous operator equations A^*AC = αA^*A² + βAA^*A and AA^*C = λA^*A² + 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(?)D of operators to be quasinormal.