Nonatomic Lipschitz spaces

Nik Weaver

Studia Mathematica (1995)

  • Volume: 115, Issue: 3, page 277-289
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Weaver, Nik. "Nonatomic Lipschitz spaces." Studia Mathematica 115.3 (1995): 277-289. <http://eudml.org/doc/216213>.

@article{Weaver1995,
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.},
author = {Weaver, Nik},
journal = {Studia Mathematica},
keywords = {Lipschitz spaces; lattice-complete unit ball; separating family of pure normal states},
language = {eng},
number = {3},
pages = {277-289},
title = {Nonatomic Lipschitz spaces},
url = {http://eudml.org/doc/216213},
volume = {115},
year = {1995},
}

TY - JOUR
AU - Weaver, Nik
TI - Nonatomic Lipschitz spaces
JO - Studia Mathematica
PY - 1995
VL - 115
IS - 3
SP - 277
EP - 289
AB - 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.
LA - eng
KW - Lipschitz spaces; lattice-complete unit ball; separating family of pure normal states
UR - http://eudml.org/doc/216213
ER -

References

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  1. [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. Zbl0634.46042
  2. [2] A. Connes, Compact metric spaces, Fredholm modules, and hyperfiniteness, Ergodic Theory Dynam. Systems 9 (1989), 207-220. Zbl0718.46051
  3. [3] K. de Leeuw, Banach spaces of Lipschitz functions, Studia Math. 21 (1961), 55-66. Zbl0101.08901
  4. [4] J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien, Gauthier-Villars, 1957. Zbl0088.32304
  5. [5] J. A. Johnson, Banach spaces of Lipschitz functions and vector-valued Lipschitz functions, Trans. Amer. Math. Soc. 148 (1970), 147-169. Zbl0194.43603
  6. [6] R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. I, Academic Press, 1983. Zbl0518.46046
  7. [7] W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces, Vol. I, North-Holland, 1971. Zbl0231.46014
  8. [8] D. R. Sherbert, Banach algebras of Lipschitz functions, Pacific J. Math. 13 (1963), 1387-1399. Zbl0121.10203
  9. [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. Zbl0121.10204
  10. [10] L. Waelbroeck, Closed ideals of Lipschitz functions, in: Function Algebras, F. T. Birtel (ed.), Scott, Foresman and Co., 1966, 322-325. 
  11. [11] N. Weaver, Lattices of Lipschitz functions, Pacific J. Math. 164 (1994), 179-193. Zbl0797.46007
  12. [12] N. Weaver, Isometries of noncompact Lipschitz spaces, Canad. Math. Bull., to appear. Zbl0831.46007
  13. [13] N. Weaver, Order-completeness in Lipschitz algebras, J. Funct. Anal., to appear. Zbl0922.46022

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