Proposition 4.4 . [00LR]

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Proposition 4.4.

For any $\epsilon>0$ , there exist a homomorphism of Banach $k$ -algebras

\theta(\epsilon/2)_{W_{\epsilon/2}}:\mathcal{W}_{\epsilon/2}\rightarrow\widehat{V}_{{\scriptscriptstyle\bullet}}(L_{X|Y},\phi_{X|Y})

which extends the identity map on the dense sub- $k$ -algebra $V_{{\scriptscriptstyle\bullet}}(L_{X|Y})$ .