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arXiv · 0708.2899

A rigidity theorem for holomorphic generators on the Hilbert ball

Mark Elin·Marina Levenshtein·Simeon Reich·David Shoikhet
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Abstract

We present a rigidity property of holomorphic generators on the open unit ball $\mathbb{B}$ of a Hilbert space $H$. Namely, if $f\in\Hol (\mathbb{B},H)$ is the generator of a one-parameter continuous semigroup ${F_t}_{t\geq 0}$ on $\mathbb{B}$ such that for some boundary point $τ\in \partial\mathbb{B}$, the admissible limit $K$-$\lim\limits_{z\toτ}\frac{f(x)}{\|x-τ\|^{3}}=0$, then $f$ vanishes identically on $\mathbb{B}$.

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Mark Elin, Marina Levenshtein, Simeon Reich, David Shoikhet. 2007-08-21. A rigidity theorem for holomorphic generators on the Hilbert ball. https://arxiv.org/abs/0708.2899

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