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Spectral flow for nonunital spectral triples

Journal Article


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Abstract


  • We prove two results about nonunital index theory left open in a previous paper. The first is that the spectral triple arising from an action of the reals on a C*-algebra with invariant trace satisfies the hypotheses of the nonunital local index formula. The second result concerns the meaning of spectral flow in the nonunital case. For the special case of paths arising from the odd index pairing for smooth spectral triples in the nonunital setting, we are able to connect with earlier approaches to the analytic definition of spectral flow.

Authors


  •   Carey, Alan L.
  •   Gayral, Victor (external author)
  •   Phillips, John (external author)
  •   Rennie, Adam C.
  •   Sukochev, F A. (external author)

Publication Date


  • 2015

Citation


  • Carey, A. L., Gayral, V., Phillips, J., Rennie, A. & Sukochev, F. A. (2015). Spectral flow for nonunital spectral triples. Canadian Journal of Mathematics, 67 (4), 759-794.

Scopus Eid


  • 2-s2.0-84975841274

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6321&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5293

Number Of Pages


  • 35

Start Page


  • 759

End Page


  • 794

Volume


  • 67

Issue


  • 4

Abstract


  • We prove two results about nonunital index theory left open in a previous paper. The first is that the spectral triple arising from an action of the reals on a C*-algebra with invariant trace satisfies the hypotheses of the nonunital local index formula. The second result concerns the meaning of spectral flow in the nonunital case. For the special case of paths arising from the odd index pairing for smooth spectral triples in the nonunital setting, we are able to connect with earlier approaches to the analytic definition of spectral flow.

Authors


  •   Carey, Alan L.
  •   Gayral, Victor (external author)
  •   Phillips, John (external author)
  •   Rennie, Adam C.
  •   Sukochev, F A. (external author)

Publication Date


  • 2015

Citation


  • Carey, A. L., Gayral, V., Phillips, J., Rennie, A. & Sukochev, F. A. (2015). Spectral flow for nonunital spectral triples. Canadian Journal of Mathematics, 67 (4), 759-794.

Scopus Eid


  • 2-s2.0-84975841274

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6321&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5293

Number Of Pages


  • 35

Start Page


  • 759

End Page


  • 794

Volume


  • 67

Issue


  • 4