| 侯晋川.算子方程的解及算子张量积[J].数学研究及应用,1992,12(4):479~486 |
| 算子方程的解及算子张量积 |
| Solution of Opertor Equations and Tensor products |
| 投稿时间：1989-11-21 |
| DOI：10.3770/j.issn:1000-341X.1992.04.001 |
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| 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(?)…(?)An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. |
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