diff --git a/src/fa/norm/ap.tex b/src/fa/norm/ap.tex index 6f61758..1a0b7f2 100644 --- a/src/fa/norm/ap.tex +++ b/src/fa/norm/ap.tex @@ -235,7 +235,7 @@ \begin{corollary}[Existence of Continuous Trace] \label{corollary:trace-existence-approx} - Let $E$ a Banach spaces over $K \in \RC$ with the approximation property, then there exists a unique $\tr \in N(E; E)^*$ such that for each $\phi \in E^*$ and $x \in E$, $\tr(\phi \otimes y) = \dpn{y, \phi}{E}$. + Let $E$ a Banach space over $K \in \RC$ with the approximation property, then there exists a unique $\tr \in N(E; E)^*$ such that for each $\phi \in E^*$ and $x \in E$, $\tr(\phi \otimes y) = \dpn{y, \phi}{E}$. \end{corollary} \begin{proof} By (U) of the \hyperref[projective tensor product]{definition:projective-tensor-product} and the isomorphism $E^* \wh \otimes_\pi E \iso N(E; E)$ from \autoref{corollary:approximation-property-nuclear}.