This is an announcement for the paper "Biseparating maps between Lipschitz function spaces" by Jesus Araujo and Luis Dubarbie.

Abstract: For complete metric spaces $X$ and $Y$, a description of linear biseparating maps between spaces of vector-valued Lipschitz functions defined on $X$ and $Y$ is provided. In particular it is proved that $X$ and $Y$ are bi-Lipschitz homeomorphic, and the automatic continuity of such maps is derived in some cases. Besides, these results are used to characterize the separating bijections between scalar-valued Lipschitz function spaces when $Y$ is compact.

Archive classification: math.FA

Mathematics Subject Classification: Primary 47B38; Secondary 46E40, 46H40, 47B33

Remarks: 17 pages; no figures

The source file(s), lipschitz86.tex: 48992 bytes, is(are) stored in gzipped form as 0807.3835.gz with size 14kb. The corresponding postcript file has gzipped size 106kb.

Submitted from: araujoj@unican.es

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http://front.math.ucdavis.edu/0807.3835

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http://arXiv.org/abs/0807.3835

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