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arXiv · 2202.01853

Posinormal Composition Operators on $H^2$

Paul S. Bourdon·Derek Thompson
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Abstract

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 $C_\varphi$ on the Hardy space $H^2$ of the open unit disk $\mathbb{D}$ when $\varphi$ 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.

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BibTeXRIS

Paul S. Bourdon, Derek Thompson. 2022-02-03. Posinormal Composition Operators on $H^2$. https://arxiv.org/abs/2202.01853

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