Corollary 3.27 . [00LG]

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Corollary 3.27.

Let $\phi$ be a asymptotic Fubini-Study metric on $L$ . Then on $V_{{\scriptscriptstyle\bullet}}(L_{X|Y})$ , the spectral algebra seminorm of $\vvvert\mathord{\cdot}\vvvert_{\phi,X|Y}$ is equal to $\vvvert\mathord{\cdot}\vvvert_{\phi|_{Y}}$ . There exists a canonical homeomorphism

\mathfrak{M}(\widehat{V}_{{\scriptscriptstyle\bullet}}(L_{X|Y},\phi_{X|Y}))\simeq\mathfrak{M}(\widehat{V}_{{\scriptscriptstyle\bullet}}(L_{X|Y},\phi|_{Y})).