In this article, we characterize absolutely norm attaining normal operators in terms of the essential spectrum. Later we prove a structure theorem for hyponormal absolutely norm attaining (or $\mathcal{AN}$-operators in short) and deduce conditions for the normality of the operator.

中文翻译：

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超正态绝对范数获得算子的表示

在本文中，我们根据基本谱描述了绝对范数获得正规算子的特征。稍后我们证明了次正规绝对范数达到的结构定理（或$\mathcal{一个}$- 运算符）并推导出运算符的正态性条件。