Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Isometries between function spaces

Authors: Krzysztof Jarosz and Vijay D. Pathak
Journal: Trans. Amer. Math. Soc. 305 (1988), 193-206
MSC: Primary 46E15; Secondary 46J15
MathSciNet review: 920154
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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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Article copyright: © Copyright 1988 American Mathematical Society