Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 Dynam. Systems 9 (1989), no. 2, 207–220. MR 1007407, https://doi.org/10.1017/S0143385700004934
  • [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, New York, 1992, pp. 53–93. MR 1204452
  • [3] Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L85

Retrieve articles in all journals with MSC: 46L85


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