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 | References | Similar Articles | Additional Information
Abstract: A. Connes has shown that a unital 
-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.
- [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
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1995-1213868-4
Keywords:
Noncommutative topology,
noncommutative geometry,
automorphisms of 
-algebras
Article copyright:
© Copyright 1995
American Mathematical Society