Abstract
We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a * -subalgebra A of a general semifinite von Neumann algebra. The proof is a variant of that for the odd case which appears in Part I. To allow for algebras with a non-trivial centre we have to establish a theory of unbounded Fredholm operators in a general semifinite von Neumann algebra and in particular prove a generalised McKean–Singer formula.
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