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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 

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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