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)



The index of normal Fredholm elements of $ C\sp *$-algebras

Authors: J. A. Mingo and J. S. Spielberg
Journal: Proc. Amer. Math. Soc. 113 (1991), 187-192
MSC: Primary 46L80; Secondary 19K56, 46L05
MathSciNet review: 1045144
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Examples are given of normal elements of $ {C^*}$-algebras that are invertible modulo an ideal and have nonzero index, in contrast to the case of Fredholm operators on Hilbert space. It is shown that this phenomenon occurs only along the lines of these examples.

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

  • [1] M. F. Atiyah, Bott periodicity and the index of elliptic operators, Quart. J. Math. Oxford Ser. (2) 19 (1968), 113–140. MR 0228000,
  • [2] Bruce Blackadar, 𝐾-theory for operator algebras, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986. MR 859867
  • [3] G. A. Elliott and T. A. Loring, AF embeddings of $ C({{\mathbf{T}}^2})$ with prescribed $ K$-theory, preprint.
  • [4] R. Exel and T. A. Loring, Extending cellular cohomology to $ {C^*}$-algebras, preprint.
  • [5] Nigel Higson, A characterization of 𝐾𝐾-theory, Pacific J. Math. 126 (1987), no. 2, 253–276. MR 869779
  • [6] Terry A. Loring, The 𝐾-theory of AF embeddings of the rational rotation algebras, 𝐾-Theory 4 (1991), no. 3, 227–243. MR 1106954,
  • [7] Gert K. Pedersen, 𝐶*-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006
  • [8] M. Pimsner, S. Popa, and D. Voiculescu, Homogeneous 𝐶*-extensions of 𝐶(𝑋)⊗𝐾(𝐻). I, J. Operator Theory 1 (1979), no. 1, 55–108. MR 526291
  • [9] N. E. Wegge-Olsen, Introduction to operator algebra $ K$-theory and qeneralized index theory, preprint, Kobenhavns Universitet Matematisk Institut, 1989.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L80, 19K56, 46L05

Retrieve articles in all journals with MSC: 46L80, 19K56, 46L05

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society