Isometries of unbounded Fredholm modules over reduced group 𝐶*-algebras

Park, Efton

doi:10.1090/S0002-9939-1995-1249887-1

Isometries of unbounded Fredholm modules over reduced group $C^ \ast$-algebras
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by Efton Park

Proc. Amer. Math. Soc. 123 (1995), 1839-1843

DOI: https://doi.org/10.1090/S0002-9939-1995-1249887-1

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Abstract:

In an earlier paper, the author defined the isometry group of an unbounded Fredholm module over a unital ${C^ \ast }$-algebra. In this paper, the author studies a class of unbounded Fredholm modules over a reduced group ${C^ \ast }$-algebra, and he shows that the isometry groups of these unbounded Fredholm modules are always compact Lie groups. The author also proves a result about the fixed point algebra of such an isometry.

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
Efton Park, Isometries of noncommutative metric spaces, Proc. Amer. Math. Soc. 123 (1995), no. 1, 97–105. MR 1213868, DOI 10.1090/S0002-9939-1995-1213868-4