^{1} Department of Mathematics and Computer Science (IMADA), Faculty of Science, SDU^{2} Mathematics, Department of Mathematics and Computer Science (IMADA), Faculty of Science, SDU^{3} unknown^{4} Department of Mathematics and Computer Science (IMADA), Faculty of Science, SDU

DOI:

10.1017/is012003003jkt185

Abstract:

We present a definition of spectral flow for any norm closed ideal J in any von Neumann algebra N. Given a path of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in Ko (J). Given a semifinite spectral triple (A, H, D) relative to (N, t) with A separable, we construct a class [D] ¿ KK1 (A, K(N)). For a unitary u ¿ A, the von Neumann spectral flow between D and u*Du is equal to the Kasparov product [u] A[D], and is simply related to the numerical spectral flow, and a refined C* -spectral flow.