Perturbations of the rotation \(C^*\)-algebras and of the Heisenberg commutation relation

DOI10.1215/S0012-7094-95-07720-5zbMath0830.46058MaRDI QIDQ1896001

Mikael Rørdam, Uffe Haagerup

Publication date: 4 February 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Cuntz algebracommutation relationsVoiculescu matricesperturbation of unitaries

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55)

Related Items (21)

The quantum Gromov-Hausdorff propinquity ⋮ Singular integrals in quantum Euclidean spaces ⋮ A separable Brown-Douglas-Fillmore theorem and weak stability ⋮ The classification of Rokhlin flows on \(\mathrm{C}^*\)-algebras ⋮ Harmonic analysis approach to Gromov-Hausdorff convergence for noncommutative tori ⋮ Spectral edge regularity of magnetic Hamiltonians ⋮ Bounded perturbations of the Heisenberg commutation relation via dilation theory ⋮ On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schrödinger operators ⋮ Classification of uniformly outer actions of \(\mathbb Z^2\) on UHF algebras ⋮ On the spectrum of certain discrete Schrödinger operators with quasiperiodic potential ⋮ Dilation theory: a guided tour ⋮ Non-commutative entropy computations for continuous fields and cross-products ⋮ Wandering vectors for irrational rotation unitary systems ⋮ Classification of outer actions of \(\mathbb Z ^N\) on \(\mathcal O _2\) ⋮ \(\mathbb Z^2\)-actions on Kirchberg algebras ⋮ Norm estimates of almost Mathieu operators ⋮ A weak homotopy equivalence type result related to Kirchberg algebras ⋮ Spectral relationships between kicked Harper and on-resonance double kicked rotor operators ⋮ On the Regularity of the Hausdorff Distance Between Spectra of Perturbed Magnetic Hamiltonians ⋮ An introduction to 3D discrete magnetic Laplacians and noncommutative 3-tori ⋮ Dilations of unitary tuples

Cites Work

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• The soft torus and applications to almost commuting matrices
• Gauss polynomials and the rotation algebra
• K-theory for certain C*-algebras
• Homomorphisms of C* algebras to finite AW* algebras
• AF embeddings of \(C(\mathbb{T}^ 2)\) with a prescribed \(K\)-theory
• Extending states on preordered semigroups and the existence of quasitraces on \(C^ \ast\)-algebras
• Simple \(C^*\)-algebras generated by isometries
• The homotopy type of the unitary group of Hilbert space
• Quasitraces on exact C*-algebras are traces
• The Cancellation Theorem for Projective Modules Over Irrational Rotation C*-Algebras
• K-Theory and Asymptotically Commuting Matrices
• Almost Commuting Matrices Need not be Nearly Commuting
• Almost Commuting Unitary Matrices

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