论文标题
$ h^2 $上的正态构图运算符
Posinormal Composition Operators on $H^2$
论文作者
论文摘要
如果存在一个正算子$ p $，则希尔伯特空间上有界的线性运算符$ a $是正常的。 $ a $的正常性等同于包含$ a $ $ a $ a^*$的范围。每个不正常的操作员都是正常的，每个可逆操作员都是正常的。我们表征了hardy space上的正常和共肾形成量$c_φ$ $ h^2 $的开放单位磁盘$ \ mathbb {d} $时，$φ$是$ \ mathbb {d} $的线性折叠自我图。我们的工作表明，有一些构图算子既是正态和共同构型，但具有无法正常的力量。
A bounded linear operator $A$ on a Hilbert space is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. Posinormality of $A$ is equivalent to the inclusion of the range of $A$ in the range of its adjoint $A^*$. Every hyponormal operator is posinormal, as is every invertible operator. We characterize both the posinormal and coposinormal composition operators $C_φ$ on the Hardy space $H^2$ of the open unit disk $\mathbb{D}$ when $φ$ is a linear-fractional selfmap of $\mathbb{D}$. Our work reveals that there are composition operators that are both posinormal and coposinormal yet have powers that fail to be posinormal.
