KK -theory and spectral flow in von Neumann algebras
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KK -theory and spectral flow in von Neumann algebras. / Kaad, Jens; Nest, Ryszard; Rennie, Adam.
I: Journal of K-Theory, Bind 10, Nr. 2, 2012, s. 241-277.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - KK -theory and spectral flow in von Neumann algebras
AU - Kaad, Jens
AU - Nest, Ryszard
AU - Rennie, Adam
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
U2 - 10.1017/is012003003jkt185
DO - 10.1017/is012003003jkt185
M3 - Journal article
VL - 10
SP - 241
EP - 277
JO - Journal of K-Theory
JF - Journal of K-Theory
SN - 1865-2433
IS - 2
ER -
ID: 45182032