换位子的共轭算子  

The Adjoint Operator of Commutators

作　　者：王晓敏 吴德玉[1] Wang Xiaomin;Wu Deyu(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《数学物理学报（A辑）》2024年第6期1426-1432,共7页Acta Mathematica Scientia

基　　金：国家自然科学基金(11561048,11761029);内蒙古自然科学基金(2023MS01011,2022ZD05)

摘　　要：该文通过运用谱方法和分块算子矩阵法,研究了两个无界算子A、B的换位子[A,B]=AB−BA的共轭算子问题.给出了关系式[A,B]∗=(AB−BA)∗=B∗A∗−A∗B∗=−[A∗,B∗]成立的充分条件.最后举例说明了结果的有效性.In this paper,the adjoint operator problem of the commutators[A,B]=AB−BA of two unbounded operators A and B is studied by the spectral theory and block operator matrix theory.The sufficient conditions for the relationship[A,B]∗=(AB−BA)∗=B∗A∗−A∗B∗=−[A∗,B∗]hold are given.In the end,concrete examples is given to illustrate the effectiveness of criterions.

关 键 词：换位子 共轭算子 谱 

分 类 号：O175.3[理学—数学]