Small into-isomorphisms between spaces of continuous functions. II

Benyamini, Yoav

doi:10.1090/S0002-9947-1983-0694391-9

Small into-isomorphisms between spaces of continuous functions. II
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Trans. Amer. Math. Soc. 277 (1983), 825-833 Request permission

Abstract:

We construct two compact Hausdorff spaces, $X$ and $Y$, so that $C(X)$ does not embed isometrically into $C(Y)$, but for each $\varepsilon > 0$, there is an isomorphism ${T_\varepsilon }$ from $C(X)$ into $C(Y)$ satisfying $\parallel f\parallel \leqslant \parallel {T_\varepsilon }f\;\parallel \leqslant (1 + \varepsilon )\parallel f\parallel$ for all $f \in C(X)$.

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