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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Isometries of noncommutative metric spaces
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by Efton Park PDF
Proc. Amer. Math. Soc. 123 (1995), 97-105 Request permission

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
  • A. Connes, Compact metric spaces, Fredholm modules, and hyperfiniteness, Ergodic Theory Dynam. Systems 9 (1989), no. 2, 207–220. MR 1007407, DOI 10.1017/S0143385700004934
  • 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
  • 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
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • 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