KK -theory and spectral flow in von Neumann algebras

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Standard

KK -theory and spectral flow in von Neumann algebras. / Kaad, Jens; Nest, Ryszard; Rennie, Adam.

In: Journal of K-Theory, Vol. 10, No. 2, 2012, p. 241-277.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Kaad, J, Nest, R & Rennie, A 2012, 'KK -theory and spectral flow in von Neumann algebras', Journal of K-Theory, vol. 10, no. 2, pp. 241-277. https://doi.org/10.1017/is012003003jkt185

APA

Kaad, J., Nest, R., & Rennie, A. (2012). KK -theory and spectral flow in von Neumann algebras. Journal of K-Theory, 10(2), 241-277. https://doi.org/10.1017/is012003003jkt185

Vancouver

Kaad J, Nest R, Rennie A. KK -theory and spectral flow in von Neumann algebras. Journal of K-Theory. 2012;10(2):241-277. https://doi.org/10.1017/is012003003jkt185

Author

Kaad, Jens ; Nest, Ryszard ; Rennie, Adam. / KK -theory and spectral flow in von Neumann algebras. In: Journal of K-Theory. 2012 ; Vol. 10, No. 2. pp. 241-277.

Bibtex

@article{211b85f3a7384c07b3609766baddc25e,
title = "KK -theory and spectral flow in von Neumann algebras",
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.",
author = "Jens Kaad and Ryszard Nest and Adam Rennie",
year = "2012",
doi = "10.1017/is012003003jkt185",
language = "English",
volume = "10",
pages = "241--277",
journal = "Journal of K-Theory",
issn = "1865-2433",
publisher = "Cambridge University Press",
number = "2",

}

RIS

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