## Hyperexpansive composition operators.(English)Zbl 1066.47028

Let $$T: D(H)\to H$$ be a linear map defined on a linear subspace $$D(H)$$ of a Hilbert space $$H$$ and let $\Theta_{T,n}(f)=\sum_{0\leq p\leq n}(-1)^p{n \choose p} | | T^pf| | ^2, \; f\in D(T^n),\quad n\geq 1.$ $$T$$ is called $$k$$-hyperexpansive if $$\Theta_{T,n}(f)\leq 0$$ for $$f\in D(T^n)$$ and $$n=1,\dots,k$$, and completely hyperexpansive if $$\Theta_{T,n}(f)\leq 0$$ for $$f\in D(T^n)$$ and all $$n\geq 1$$. The author studies bounded and unbounded hyperexpansive composition operators on measure spaces $$L^2(\mu)$$.

### MSC:

 47B33 Linear composition operators

### Keywords:

hyperexpansive composition operators; measure spaces
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