KK-theory and Spectral Flow in von Neumann Algebras

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dc.creatorKaad, Jens
dc.creatorNest, Ryszard
dc.creatorRennie, Adam
dc.date2007-01-11
dc.date.accessioned2026-07-07T07:40:02Z
dc.date.available2026-07-07T07:40:02Z
dc.descriptionWe present a definition of spectral flow relative to any norm closed ideal J in any von Neumann algebra N. Given a path D(t) of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in K_0(J). In the case when N is semifinite, the numerical spectral flow of the path coincides with the value of trace on the associated K-class. Given a semifinite spectral triple (A,H,D) relative to a semifinite von Neumann algebra N, we construct a class [D] in KK^1(A,N') such that, for a unitary u in A, the von Neumann spectral flow between D and u*Du is equal to the Kasparov product of [u] and [D].
dc.identifierhttps://arxiv.org/abs/math/0701326
dc.identifierhttp://arxiv.org/abs/math/0701326
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121666
dc.subjectOperator Algebras
dc.titleKK-theory and Spectral Flow in von Neumann Algebras
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