U-标算子的结构分析  

The Structural Analysis of U-Scalar Operators

作　　者：孙万贵[1] 

机构地区：[1]西北大学经济管理学院,西安710069

出　　处：《数学学报（中文版）》2006年第2期465-468,共4页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10271097)

摘　　要：类似与标型谱算子,U-标算子是否拟仿射相似于自伴算子是一“公开问题”．尽管对具纯离散谱的U-标算子答案是肯定的,但一般情况下并不成立．本文继续探讨这一问题,证明了U-标算子在一强范数拓扑意义下是Hermite算子,或者说U-标算子拟仿射相似于Hermite算子,并给出U-标算子是标型谱算子的充要条件．Whether a U-scalar operator is a quasi-affine transform of a self-adjoint operator, similar to a spectral operator of scalar type, is an open question. Although it holds true for the U-scalar operator with purely discrete spectrum, the question, generally speaking, is negative. The aim of this paper is to address this problem. It is proved that a U-scalar operator in a Hilbert space is a Hermitian operator in the sense of a strong-norm topology, and the necessary and sufficient conditions are given under which a U-scalar operator is a spectral operator of scalar type.

关 键 词：U-标算子 Hermite算子 标型谱算子 

分 类 号：O177.2[理学—数学]