Unbounded Fredholm modules and double operator integrals

DOI10.1515/CRELLE.2009.006zbMath1189.46063MaRDI QIDQ3600028

Denis Potapov, Pheodor A. Sukochev

Publication date: 10 February 2009

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

zbMATH Keywords

noncommutative geometryDirac operatorspectral tripleFredholm modules

Mathematics Subject Classification ID

Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Related Items (27)

\(L_p\)-bounds for the Krein spectral shift function: \(0<p<\infty\) ⋮ Universal measurability and the Hochschild class of the Chern character ⋮ Schatten class estimates for the Riesz map of massless Dirac operators ⋮ Quantum differentiability of essentially bounded functions on Euclidean space ⋮ Spectral shift function of higher order ⋮ On the Witten index in terms of spectral shift functions ⋮ The Witten index and the spectral shift function ⋮ Approximation of the spectral action functional in the case of \(\tau\)-compact resolvents ⋮ Endpoint weak Schatten class estimates and trace formula for commutators of Riesz transforms with multipliers on Heisenberg groups ⋮ Spectral estimates and asymptotics for stratified Lie groups ⋮ Operator θ$\theta$‐Hölder functions with respect to ∥·∥p$\Vert \cdot \Vert _p$, 0<p⩽∞$0&lt; p\leqslant \infty$ ⋮ Operator-Lipschitz functions in Schatten-von Neumann classes ⋮ Trace theorem for quasi-Fuchsian groups ⋮ Integration on locally compact noncommutative spaces ⋮ Weak type operator Lipschitz and commutator estimates for commuting tuples ⋮ Advances in Dixmier traces and applications ⋮ Sign of a perturbed massive Dirac operator and associated Fredholm module ⋮ Fréchet differentiability of \(\mathcal{S}^p\) norms ⋮ Asymptotic expansions for trace functionals ⋮ The index formula and the spectral shift function for relatively trace class perturbations ⋮ Quantum differentiability on noncommutative Euclidean spaces ⋮ Quantum differentiability on quantum tori ⋮ Functions of operators under perturbations of class \(S_p\) ⋮ Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators ⋮ Weak \((1,1)\) estimates for multiple operator integrals and generalized absolute value functions ⋮ Operator \(\theta\)-Hölder functions ⋮ Arithmetic-geometric mean and related submajorisation and norm inequalities for \(\tau\)-measurable operators. II

Cites Work

• Non-commutative Banach function spaces
• Notes on non-commutative integration
• On unbounded \(p\)-summable Fredholm modules
• Classification of simple \(C^*\)-algebras: Inductive limits of matrix algebras over one-dimensional spaces
• Spectral flow in Fredholm modules, eta invariants and the JLO cocycle
• Spectral flow and Dixmier traces
• The Hochschild class of the Chern character for semifinite spectral triples
• A complete set of numerical invariants for a subfactor
• The local index formula in noncommutative geometry
• Type II non-commutative geometry. I: Dixmier trace in von Neumann algebras
• Noncommutative Kothe Duality
• COMMUTATOR ESTIMATES AND $\RR$-FLOWS IN NON-COMMUTATIVE OPERATOR SPACES

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