Connes integration formula for the noncommutative plane

DOI10.1007/s00220-017-3008-5zbMath1396.46054arXiv1703.04256OpenAlexW2606012674MaRDI QIDQ1749349

Dmitriy Zanin, Pheodor A. Sukochev

Publication date: 16 May 2018

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.04256

zbMATH Keywords

singular tracesintegration formulanoncommutative (Moyal) plane

Mathematics Subject Classification ID

Noncommutative topology (46L85) Noncommutative differential geometry (46L87)

Related Items (13)

Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori ⋮ Weyl's laws and Connes' integration formulas for matrix-valued \(L\!\log \!L\)-Orlicz potentials ⋮ Schatten class estimates for the Riesz map of massless Dirac operators ⋮ A noncommutative Tauberian theorem and Weyl asymptotics in noncommutative geometry ⋮ Noncommutative geometry for symmetric non-self-adjoint operators ⋮ A \(C^*\)-algebraic approach to the principal symbol. II ⋮ Spectral shift for relative Schatten class perturbations ⋮ Algebraic Calderón-Zygmund theory ⋮ Advances in Dixmier traces and applications ⋮ Quantum differentiability on noncommutative Euclidean spaces ⋮ An operator-valued \(T1\) theory for symmetric CZOs ⋮ A Dixmier trace formula for the density of states ⋮ Dixmier trace formulas and negative eigenvalues of Schrödinger operators on curved noncommutative tori

Cites Work

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• Fubini theorem in noncommutative geometry
• Singular traces. Theory and applications
• Integration on locally compact noncommutative spaces
• Moyal planes are spectral triples
• Banach limits and traces on \(\mathcal{L}_{1, \infty}\)
• Measures from Dixmier traces and zeta functions
• About the Banach envelope of \(l_{1,\infty}\)
• The action functional in non-commutative geometry
• On summability of distributions and spectral geometry
• Commutator structure of operator ideals
• Traces of compact operators and the noncommutative residue
• Type II non-commutative geometry. I: Dixmier trace in von Neumann algebras
• Index theory for locally compact noncommutative geometries
• Traces and Shift Invariant Functionals
• Cwikel estimates revisited

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