Continuity of the spectrum of Dirac operators of spectral triples for the spectral propinquity

DOI10.1007/S00208-023-02659-XMaRDI QIDQ6499966

Frédéric Latrémolière

Publication date: 10 May 2024

Published in: Mathematische Annalen (Search for Journal in Brave)

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Noncommutative differential geometry (46L87) One-parameter semigroups and linear evolution equations (47D06) Applications of operator algebras to the sciences (47L90) Abstract operator algebras on Hilbert spaces (47L30) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Noncommutative geometry methods in quantum field theory (81T75) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Noncommutative geometry in quantum theory (81R60) Operator algebra methods applied to problems in quantum theory (81R15) Noncommutative geometry (à la Connes) (58B34) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) States of selfadjoint operator algebras (46L30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equivalence of quantum metrics with a common domain
• The dual Gromov-Hausdorff propinquity
• Gravity coupled with matter and the foundation of non-commutative geometry
• The Dirac operator on \(\text{SU}_{q}(2)\)
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Metrics on states from actions of compact groups
• The spectral action principle
• Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples
• Noncommutative geometry and matrix theory: Compactification on tori
• String theory and noncommutative geometry
• Collapsing and Dirac-type operators
• The Podleś sphere as a spectral metric space
• Convergence of Cauchy sequences for the covariant Gromov-Hausdorff propinquity
• Metrics on state spaces
• Collapsing and the differential form Laplacian: the case of a smooth limit space.
• Group \(C^*\)-algebras as compact quantum metric spaces
• Quantum locally compact metric spaces
• Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves
• The dual modular Gromov-Hausdorff propinquity and completeness
• Convergence of spectral triples on fuzzy tori to spectral triples on quantum tori
• Dirac operators and geodesic metric on the harmonic Sierpiński gasket and other fractal sets
• The Dirac operator under collapse to a smooth limit space
• Convergence of spectral structures: a functional analytic theory and its applications to spectral geometry
• Collapsing with a lower bound on the curvature operator
• Generalized fuzzy torus and its modular properties
• Bounded-Lipschitz distances on the state space of a \(C^*\)-algebra
• Dirac operators and spectral triples for some fractal sets built on curves
• The Gromov-Hausdorff propinquity for metric spectral triples
• Quantum ultrametrics on AF algebras and the Gromov–Hausdorff propinquity
• On noncommutative geometry of orbifolds
• On Spectral Triples on Crossed Products Arising From Equicontinuous Actions
• Matrix geometries and fuzzy spaces as finite spectral triples
• Convergence of Fuzzy Tori and Quantum Tori for the quantum Gromov-Hausdorff Propinquity: an explicit approach
• Nilpotent Group C*-algebras as Compact Quantum Metric Spaces
• The triangle inequality and the dual Gromov-Hausdorff propinquity
• Hyperbolic Group C^*-Algebras and Free-Product C^*-Algebras as Compact Quantum Metric Spaces
• The quantum Gromov-Hausdorff propinquity
• Curved noncommutative tori as Leibniz quantum compact metric spaces
• Gromov-Hausdorff distance for quantum metric spaces
• A compactness theorem for the dual Gromov-Hausdorff propinquity
• Noncommutative Cosmology
• The modular Gromov–Hausdorff propinquity
• The covariant Gromov–Hausdorff propinquity
• Matricial bridges for “Matrix algebras converge to the sphere”
• Compact metric spaces, Fredholm modules, and hyperfiniteness
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Noncommutative gauge theory on fuzzy sphere from matrix model

This page was built for publication: Continuity of the spectrum of Dirac operators of spectral triples for the spectral propinquity