Index of Nonlocal Operators over C*-Algebras

Part of the Operator Theory: Advances and Applications book series (OT, volume 183)


In this chapter, we obtain index formulas for nonlocal elliptic operators D = (D, P1, P2) over some C*-algebra Λ.1 As in the Mishchenko-Fomenko index theory [57], where one considers the index of local elliptic operators over C*-algebras and whose ideology we follow to a large extent here, the main role in the structure and the proof of such index formulas is played by the Künneth formula describing the K-group of tensor products of C*-algebras. To ensure that the Künneth formula applies, we assume throughout the chapter that the algebra Λ belongs to the so-called class N (bootstrap class) in the sense of [66]. Let us recall the definition of this class.


Tensor Product Exact Sequence Projective Module Topological Index Index Theorem 
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© Birkhäuser Verlag AG 2008

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