I want to prove that for Banach space V there is a compact topological space $X$ so that $V$ is isometrically isomorphic to a closed subspace of $C(X)$-continuous function on a (compact) topological space X, equipped with the supremum norm $\|f\|_\infty$ = $\sup_{x \in X} |f(x)|$.
For Banach space there is a compact topological space so that the Banach space is isometrically isomorphic with a closed subspace of $C(X)$.
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functional-analysis
vector-spaces
banach-spaces