论文标题
在平均变换的图像上
On the image of the mean transform
论文作者
论文摘要
令$ b（h）$为Hilbert Space $ h $上所有有界运营商的代数。令$ t = v | t | $是b（h）$中运算符$ t \的极性分解。 $ t $的平均转换由$ m（t）= \ frac {t+| t | v} {2} $定义。在本文中，我们讨论了与频谱，内核，图像，平均变换的极性分解有关的几种属性。此外，我们通过某些类算子的平均变换为正，正常，统一，不正常和夏威太射算子来研究图像和预先图像。
Let $B(H)$ be the algebra of all bounded operators on a Hilbert space $H$. Let $T=V|T|$ be the polar decomposition of an operator $T\in B(H)$. The mean transform of $T$ is defined by $M(T)=\frac{T+|T|V}{2}$. In this paper, we discuss several properties related to the spectrum, the kernel, the image, the polar decomposition of mean transform. Moreover, we investigate the image and preimage by the mean transform of some class of operators as positive, normal, unitary, hyponormal and co-hyponormal operators.
