%0 Journal Article
%T A rigidity theorem for holomorphic generators on the Hilbert ball
%A Mark Elin
%A Marina Levenshtein
%A Simeon Reich
%A David Shoikhet
%J Mathematics
%D 2007
%I arXiv
%X 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 $\tau\in \partial\mathbb{B}$, the admissible limit $K$-$\lim\limits_{z\to\tau}\frac{f(x)}{\|x-\tau\|^{3}}=0$, then $f$ vanishes identically on $\mathbb{B}$.
%U http://arxiv.org/abs/0708.2899v1