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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
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)
关键词
U-标算子
Hermite算子
标型谱算子
U-scalar operator
Hermitian oDerator
sDectral operator of scalar tvne
