论文标题
$ m $ isometries的Aluthge和平均变换
The Aluthge and the mean transforms of $m$-isometries
论文作者
论文摘要
令$ t \在b（h）$中为Hilbert Space $ H $上的有界线性运算符，令$ t = V | t | $为$ t $的极地分解，让$λ\在[0,1] $中。 $λ$ -Arthge变换$Δ_λ（t）$和平均值转换$ m（t）$分别由：\ [δ_λ（t）：= | = | t | t | t |^λv| t | t |^|^{1-λ} \; \; \; \ text {and} \; \; m（t）：= \ frac12（| t | v+v | t |）。\ \]在本文中，我们使用了几个加权移动运算符的示例来证明Aluthge和Mean Transforms不能在任何方向上保留$ m $ ISOMETRIES的类别。
Let $T\in B(H)$ be a bounded linear operator on a Hilbert space $H$, let $T = V|T|$ be its polar decomposition of $T$ and let $λ\in [0,1]$. The $λ$-Aluthge transform $Δ_λ(T)$ and the mean transforms $M(T)$ are defined respectively by: \[Δ_λ(T):=|T|^λV|T|^{1-λ} \;\; \text{and} \;\; M(T):=\frac12(|T|V+V|T|).\] In this paper, we use several examples of weighted shift operators to prove that the Aluthge and mean transforms do not preserve the class of $m-$isometries in any directions.
