The class of polynomially normal operators is a wider class than the class of all normal operators. Inspired by some interesting well known facts about normal operators and by some recent work, we present new properties of polynomially normal operators. Precisely, we prove that under certain conditions polynomially normal operators are Drazin or even group invertible and we also give necessary and sufficient conditions for a polynomially normal operator to have a closed range. In addition, we characterize polynomially normal operators with or without closed ranges applying the adequate operator matrix representations. Furthermore, we show that in some cases a polynomially normal operator can be written as a direct sum of a normal operator and a nilpotent operator. What is more, we state several examples to illustrate our results.

多项式正规运算符的类别比所有正规运算符的类别更广泛。受关于正规算子的一些有趣的众所周知的事实和最近的一些工作的启发，我们提出了多项式正规算子的新属性。准确地说，我们证明了在一定条件下多项式正规算子是Drazin甚至群可逆的，并且给出了多项式正规算子具有闭域的充分必要条件。此外，我们使用适当的运算符矩阵表示来表征具有或不具有闭合范围的多项式正态运算符。此外，我们表明在某些情况下，多项式正规运算符可以写成正规运算符和幂零运算符的直和。更重要的是，我们陈述了几个例子来说明我们的结果。