Locally bounded perturbations and (odd) unbounded $KK$-theory

DOI10.4171/JNCG/312zbMath1419.19003arXiv1608.02506OpenAlexW2517339878MaRDI QIDQ1731734

Koen van den Dungen

Publication date: 14 March 2019

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.02506

zbMATH Keywords

unbounded operatorself-adjoint operatorHilbert moduleapproximate identityunbounded multiplier$KK$-theory

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Commutators, derivations, elementary operators, etc. (47B47) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Kasparov theory ((KK)-theory) (19K35)

Related Items

Curvature of differentiable Hilbert modules and Kasparov modules ⋮ Noncommutative geometry for symmetric non-self-adjoint operators ⋮ Homotopy equivalence in unbounded \(KK\)-theory ⋮ Factorization of Dirac operators on almost-regular fibrations of \(\mathrm{spin}^c\) manifolds ⋮ Gauge theory on noncommutative Riemannian principal bundles ⋮ Immersions and the unbounded Kasparov product: embedding spheres into Euclidean space

Cites Work

• Nonunital spectral triples and metric completeness in unbounded \(KK\)-theory
• Pseudo-Riemannian spectral triples and the harmonic oscillator
• A local global principle for regular operators in Hilbert \(C^*\)-modules
• The \(KK\)-product of unbounded modules
• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• Unbounded bivariant \(K\)-theory and correspondences in noncommutative geometry
• Dense domains, symmetric operators and spectral triples
• Spectral flow and the unbounded Kasparov product
• Essential self-adjointness of powers of generators of hyperbolic equations
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