Theorem 3.28 . [00LI]

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Theorem 3.28.

Let $\phi$ be an asymptotic Fubini-Study metric on $L$ , then for any $\epsilon>0$ , and any $t_{1}\in V_{1}(L|_{Y})$ , there exists $n_{Y}\in\mathbb{N}$ such that for any $n\geq n_{Y}$ , there exists $s_{n}\in V_{n}(L)$ with $s_{n}|_{Y}=t_{1}^{\otimes n}$ and

\lVert s_{n}\rVert_{n\phi}\leq\mathrm{e}^{n\epsilon}\cdot(\lVert t_{1}\rVert_{\phi|_{Y}})^{n}.