Abstract:
In this paper natural generalizations are developed of the theory of elliptic operators invariant under the action of a $C^*$-algebra. The theory of compact and Fredholm operators acting in spaces of the type of a Hilbert space over a $C^*$-algebra is developed. A formula of the Atiyah–Singer type for elliptic operators over a $C^*$-algebra is developed.
Bibliography: 16 titles.
\Bibitem{MisFom79}
\by A.~S.~Mishchenko, A.~T.~Fomenko
\paper The index of elliptic operators over $C^*$-algebras
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 1
\pages 87--112
\mathnet{http://mi.mathnet.ru/eng/im1733}
\crossref{https://doi.org/10.1070/IM1980v015n01ABEH001207}
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\zmath{https://zbmath.org/?q=an:0448.46039|0416.46052}
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Bernhard Hanke, Springer Proceedings in Mathematics, 17, Global Differential Geometry, 2012, 275
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