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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 4, Pages 849–865 (Mi izv1538)  

This article is cited in 3 scientific papers (total in 3 papers)

The equivariant index of $C^*$-elliptic operators

E. V. Troitskii


Abstract: Let $G$ be a compact Lie group, and $A$$C^*$-algebra with identity. A $K$-theory of $G$-equivariant $A$-vector bundles is developed along with a corresponding theory of Fredholm operators, and the analytic and topological indices of an elliptic equivariant pseudodifferential operator over a $C^*$-algebra $A$ are defined. An index theorem generalizing the Mishchenko–Fomenko theorem is proved.
Bibliography: 19 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:1, 207–224

Bibliographic databases:

UDC: 517.98
MSC: Primary 46L80, 47A53, 55N25, 58G10, 58G12, 58G15; Secondary 14F05, 35J99, 46M20
Received: 18.06.1984

Citation: E. V. Troitskii, “The equivariant index of $C^*$-elliptic operators”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986), 849–865; Math. USSR-Izv., 29:1 (1987), 207–224

Citation in format AMSBIB
\Bibitem{Tro86}
\by E.~V.~Troitskii
\paper The equivariant index of $C^*$-elliptic operators
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 4
\pages 849--865
\mathnet{http://mi.mathnet.ru/izv1538}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=864180}
\zmath{https://zbmath.org/?q=an:0641.46047}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 1
\pages 207--224
\crossref{https://doi.org/10.1070/IM1987v029n01ABEH000967}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Troitskii, “Exact $K$-cohomological $C^*$-index formula. II. The index theorem and its applications”, Russian Math. Surveys, 44:1 (1989), 259–260  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Jonathan Rosenberg, Shmuel Weinberger, “HigherG-signatures for Lipschitz manifolds”, K-Theory, 7:2 (1993), 101  crossref  mathscinet  zmath
    3. E. V. Troitskii, “An Averaging Theorem in $C^*$-Hilbert Modules and Operators without Adjoint”, Funct. Anal. Appl., 28:3 (1994), 220–223  mathnet  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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