Noncommutative residues and a characterisation of the noncommutative integral

DOI10.1090/S0002-9939-2010-10472-0zbMath1218.58019arXiv0905.0187MaRDI QIDQ3082294

Steven Lord, Pheodor A. Sukochev

Publication date: 10 March 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.0187

zbMATH Keywords

Dixmier tracenoncommutative residuemeasurable operatorsnormal statesgeneralized zeta functions

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Noncommutative measure and integration (46L51) Noncommutative geometry (à la Connes) (58B34) Noncommutative global analysis, noncommutative residues (58J42) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items

Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics, Integration on locally compact noncommutative spaces, Advances in Dixmier traces and applications, Spectral triples and wavelets for higher-rank graphs, Measures from Dixmier traces and zeta functions

Cites Work

• Dixmier traces as singular symmetric functionals and applications to measurable operators
• Gravity coupled with matter and the foundation of non-commutative geometry
• Measures from Dixmier traces and zeta functions
• The Dixmier trace and asymptotics of zeta functions
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• The action functional in non-commutative geometry
• C*-algebras associated with irrational rotations
• Spectral flow and Dixmier traces
• Dixmier traces and some applications in non-commutative geometry
• Quantum unique ergodicity
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