Mathematics of the USSR-Izvestiya · 1980 · 188 citations · 4 references
Natural SciencesMathematicsAlgebraApplied MathematicsRepresentation TheoryAbstract AlgebraHilbert Space FormalismInvariant TheoryLinear AlgebraOperator TheoryCompact Operator TheoryCompact OperatorsFredholm OperatorsFredholm TheoryOperator AlgebrasOperator SpacesOperatorsSelf-adjoint Operators
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.
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