Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-26T08:43:00.867Z Has data issue: false hasContentIssue false

On the unique predual problem for Lipschitz spaces

Published online by Cambridge University Press:  26 July 2017

NIK WEAVER*
Affiliation:
Department of Mathematics, Washington University, Saint Louis, MO 63130, U.S.A. e-mail: [email protected]

Abstract

For any metric space X, the predual of Lip(X) is unique. If X has finite diameter or is complete and convex—in particular, if it is a Banach space—then the predual of Lip0(X) is unique.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Arens, R. F. and Eells, J. Jr., On embedding uniform and topological spaces. Pacific J. Math. 6 (1956), 397403.Google Scholar
[3] Dixmier, J. Sur un théorème de Banach. Duke Math. J. 15 (1948), 10571071.Google Scholar
[4] Dubei, M., Tymchatyn, E. D. and Zagorodnyuk, A. Free Banach spaces and extensions of Lipschitz maps. Topology 48 (2009), 203212.Google Scholar
[5] Godard, A. Tree metrics and their Lipschitz-free spaces. Proc. Amer. Math. Soc. 138 (2010), 43114320.Google Scholar
[6] Godefroy, G. and Kalton, N. J. Lipschitz-free Banach spaces. Studia Math. 159 (2003), 121141.Google Scholar
[7] Kadets, V. M. Lipschitz mappings of metric spaces. Izv. Vyssh. Uchebn. Zaved. Mat. 83 (1985), 3034.Google Scholar
[8] Sakai, S. A characterisation of W* algebras. Pacific J. Math. 6 (1956), 763773.Google Scholar
[9] Weaver, N. Lipschitz Algebras (World Scientific, 1999).Google Scholar