New York Journal of Mathematics
Volume 20 (2014) 1001-1020


Iain Forsyth, Bram Mesland, and Adam Rennie

Dense domains, symmetric operators and spectral triples

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Published: November 4, 2014
Keywords: Symmetric operator, spectral triple
Subject: 47B25, 58B34

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.


The first and third authors were supported by the Australian Research Council, while the second author was supported by the EPSRC grant EP/J006580/2.

Author information

Iain Forsyth:
Mathematical Sciences Institute, Australian National University, Canberra, Australia

Bram Mesland:
Mathematics Institute, Zeeman Building, University of Warwick,Coventry CV4 7AL, UK

Adam Rennie:
School of Mathematics and Applied Statistics, University of Wollongong Wollongong, Australia