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ArticleOriginal scientific text

Title

Nonatomic Lipschitz spaces

Authors 1

Affiliations

  1. Mathematics Department, University of California at Santa Barbara, Santa Barbara, California 93106, U.S.A.

Abstract

We abstractly characterize Lipschitz spaces in terms of having a lattice-complete unit ball and a separating family of pure normal states. We then formulate a notion of "measurable metric space" and characterize the corresponding Lipschitz spaces in terms of having a lattice complete unit ball and a separating family of normal states.

Bibliography

  1. W. G. Bade, P. C. Curtis and H. G. Dales, Amenability and weak amenability for Beurling and Lipschitz algebras, Proc. London Math. Soc. 55 (1987), 359-377.
  2. A. Connes, Compact metric spaces, Fredholm modules, and hyperfiniteness, Ergodic Theory Dynam. Systems 9 (1989), 207-220.
  3. K. de Leeuw, Banach spaces of Lipschitz functions, Studia Math. 21 (1961), 55-66.
  4. J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien, Gauthier-Villars, 1957.
  5. J. A. Johnson, Banach spaces of Lipschitz functions and vector-valued Lipschitz functions, Trans. Amer. Math. Soc. 148 (1970), 147-169.
  6. R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. I, Academic Press, 1983.
  7. W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces, Vol. I, North-Holland, 1971.
  8. D. R. Sherbert, Banach algebras of Lipschitz functions, Pacific J. Math. 13 (1963), 1387-1399.
  9. D. R. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc. 111 (1964), 240-272.
  10. L. Waelbroeck, Closed ideals of Lipschitz functions, in: Function Algebras, F. T. Birtel (ed.), Scott, Foresman and Co., 1966, 322-325.
  11. N. Weaver, Lattices of Lipschitz functions, Pacific J. Math. 164 (1994), 179-193.
  12. N. Weaver, Isometries of noncompact Lipschitz spaces, Canad. Math. Bull., to appear.
  13. N. Weaver, Order-completeness in Lipschitz algebras, J. Funct. Anal., to appear.
Studia Mathematica
1995/115/3
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Pages:
277-289
Main language of publication
English
Received
1994-11-02
Accepted
1995-03-09
Published
1995
Exact and natural sciences