摘要: 我们一般通过定义判断一个算子是否为M-亚正规算子，但证明过程较复杂。本文基于现有结论及M-亚正规算子的定义，借助谱半径、级数敛散性、矩阵乘积运算、范数计算等基础知识，得出了以有界正数序列
为权序列的单边加权移位算子不为M-亚正规算子的两类情况，结论如下：1) 若α,β,γ中有两个数相等且异于第三个数，则T不是M-亚正规算子。2) 若序列中的α,β,γ满足
，则T不是M-亚正规算子。本文提出的定理为判断一种特定类型算子是否为M-亚正规算子提供了更简单的方式。
Abstract:
We generally use the definition to judge whether an operator is M-hyponormal operator, but the process of proof is more complicated and difficult. In this paper, based on the existing conclusions and the definition of M-hyponormal operator, using the basic knowledge of spectral radius, series convergence and divergence, matrix product operation, norm calculation, etc., we obtain two kinds of cases in which the unilateral weighted shift operator with bounded positive sequence
as weight sequence is not M-hyponormal operator, the conclusions are as follows: 1) If two numbers in α,β,γ are equal and different from the third number, then T is not a M-hyponormal operator. 2) If the α,β,γ satisfy
, then T is not a M-hyponormal operator. The theorem presented in this paper provides a more convenient way to judge whether a particular type of operator is M-hyponormal operator.