酉自伴算子  

UNITARY SELF-ADJOINT OPERATORS

作　　者：袁久银[1] 

机构地区：[1]湖北民族学院计算机与数学系,恩施445000

出　　处：《湖北民族学院学报（自然科学版）》1997年第3期29-33,共5页Journal of Hubei Minzu University(Natural Science Edition)

摘　　要：受Dieudonne拟自伴算子的启发而引入了酉自伴算子．主要讨论了酉自伴算子的性质，给出了某些特殊算子为酉自伴算子的充分必要条件．另外证明了任何有界线性算子可分解为酉自伴算子和完全非酉自伴算子的直和，最后讨论了酉自伴算子的不变子空间问题．In light of Dieudonne's quasitrianglar operators,the major properties of unitary self-adjoint operators are discussed in this paper. On this basis,We obtain the sufficient and necessary conditions for some special operators to be unitary self-adjoint operators and prove that any bounded linear operatorcan be decomposed into direct sums of Unitary Self-adjoint operators and non-unitary self-adjoint operators. The question of the invariant subspace of unitary self-adjoint operators are finally discussed s well.

关 键 词：不变子空间 酉自伴算子 拟自伴算子 HILBERT空间 有界线性算子 共轭算子 

分 类 号：O177.1[理学—数学]