Isometries between function spaces

Jarosz, Krzysztof; Pathak, Vijay D.

doi:10.1090/S0002-9947-1988-0920154-7

Isometries between function spaces
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by Krzysztof Jarosz and Vijay D. Pathak PDF

Trans. Amer. Math. Soc. 305 (1988), 193-206 Request permission

Abstract:

Surjective isometries between some classical function spaces are investigated. We give a simple technical scheme which verifies whether any such isometry is given by a homeomorphism between corresponding Hausdorff compact spaces. In particular the answer is positive for the ${C^1}(X)$, $\operatorname {AC} [0,1]$, ${\operatorname {Lip} _\alpha }(X)$ and ${\operatorname {lip} _\alpha }(X)$ spaces provided with various natural norms.

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