中文摘要：

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．

英文摘要：

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.