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Isometries of noncommutative metric spaces


Author: Efton Park
Journal: Proc. Amer. Math. Soc. 123 (1995), 97-105
MSC: Primary 46L85
DOI: https://doi.org/10.1090/S0002-9939-1995-1213868-4
MathSciNet review: 1213868
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Abstract: A. Connes has shown that a unital $ {C^ \ast }$-algebra equipped with an unbounded Fredholm module can be viewed as a "noncommutative" metric space. In this paper, the author defines a notion of an isometry of a noncommutative metric space, and computes several examples.


References [Enhancements On Off] (What's this?)

  • [1] A. Connes, Compact metric spaces, Fredholm modules, and hyperfiniteness, Ergodic Theory Dynamical Systems 9 (1989), 207-220. MR 1007407 (90i:46124)
  • [2] Alain Connes and John Lott, The metric aspect of noncommutative geometry, New Symmetry Principles in Quantum Field Theory (Cargèse, 1991), NATO Adv. Sci. Inst. Ser. B Phys., vol. 295, Plenum Press, New York, 1992, pp. 53-93. MR 1204452 (93m:58011)
  • [3] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978. MR 514561 (80k:53081)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1213868-4
Keywords: Noncommutative topology, noncommutative geometry, automorphisms of $ {C^ \ast }$-algebras
Article copyright: © Copyright 1995 American Mathematical Society

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