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Dense domains, symmetric operators and spectral triples

Journal Article


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Abstract


  • This article is about erroneous attempts to weaken the standard definition of unbounded Kasparov module (or spectral triple). This issue has been addressed previously, but here we present concrete counterexamples to claims in the literature that Fredholm modules can be obtained from these weaker variations of spectral triple. Our counterexamples are constructed using self-adjoint extensions of symmetric operators.

Authors


  •   Forsyth, Iain G. (external author)
  •   Mesland, B (external author)
  •   Rennie, Adam C.

Publication Date


  • 2014

Citation


  • Forsyth, I. G., Mesland, B. & Rennie, A. C. (2014). Dense domains, symmetric operators and spectral triples. The New York Journal of Mathematics, 20 1001-1020.

Scopus Eid


  • 2-s2.0-84908671273

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4853&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3834

Number Of Pages


  • 19

Start Page


  • 1001

End Page


  • 1020

Volume


  • 20

Place Of Publication


  • http://nyjm.albany.edu/nyjm/j/2014/Vol20.htm

Abstract


  • This article is about erroneous attempts to weaken the standard definition of unbounded Kasparov module (or spectral triple). This issue has been addressed previously, but here we present concrete counterexamples to claims in the literature that Fredholm modules can be obtained from these weaker variations of spectral triple. Our counterexamples are constructed using self-adjoint extensions of symmetric operators.

Authors


  •   Forsyth, Iain G. (external author)
  •   Mesland, B (external author)
  •   Rennie, Adam C.

Publication Date


  • 2014

Citation


  • Forsyth, I. G., Mesland, B. & Rennie, A. C. (2014). Dense domains, symmetric operators and spectral triples. The New York Journal of Mathematics, 20 1001-1020.

Scopus Eid


  • 2-s2.0-84908671273

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4853&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3834

Number Of Pages


  • 19

Start Page


  • 1001

End Page


  • 1020

Volume


  • 20

Place Of Publication


  • http://nyjm.albany.edu/nyjm/j/2014/Vol20.htm