## 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.## References

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## Additional Information

- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**305**(1988), 193-206 - MSC: Primary 46E15; Secondary 46J15
- DOI: https://doi.org/10.1090/S0002-9947-1988-0920154-7
- MathSciNet review: 920154