A metric approach to limit operators

DOI10.1090/tran/6660zbMath1380.47024arXiv1408.0678OpenAlexW2963489567MaRDI QIDQ2826760

Rufus Willett, Ján Špakula

Publication date: 18 October 2016

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

Full work available at URL: https://arxiv.org/abs/1408.0678

zbMATH Keywords

Fredholm operatorlimit operatorband-dominated operatoroperator spectrumYu's property Abounded geometry strongly discrete metric space

Mathematics Subject Classification ID

Noncommutative topology (46L85) (Semi-) Fredholm operators; index theories (47A53) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Analysis on metric spaces (30L99)

Related Items (24)

The type semigroup, comparison, and almost finiteness for ample groupoids ⋮ A quasi-local characterisation of \(L^{p}\)-Roe algebras ⋮ On Persson's formula: an étale groupoid approach ⋮ On Banach algebras of band-dominated operators and their order structure ⋮ Limit operators techniques on general metric measure spaces of bounded geometry ⋮ Topological property (T) for groupoids ⋮ Expanders are counterexamples to the \(\ell^p\) coarse Baum-Connes conjecture ⋮ On the spectrum of operator families on discrete groups over minimal dynamical systems ⋮ The essential spectrum of Toeplitz operators on the unit ball ⋮ Necessary density conditions for sampling and interpolation in spectral subspaces of elliptic differential operators ⋮ Low‐dimensional properties of uniform Roe algebras ⋮ On the uniform Roe algebra as a Banach algebra and embeddings of ℓp uniform Roe algebras ⋮ Extreme cases of limit operator theory on metric spaces ⋮ Sofic boundaries of groups and coarse geometry of sofic approximations ⋮ On the essential spectrum of elliptic differential operators ⋮ Elliptic differential operators on infinite graphs with general conditions on vertices ⋮ Limit operators, compactness and essential spectra on bounded symmetric domains ⋮ Limit operator theory for groupoids ⋮ Structure and \(K\)-theory of \(\ell^p\) uniform Roe algebras ⋮ Eigenfunctions growth of \(\mathcal{R}\)-limits on graphs ⋮ Embeddings of uniform Roe algebras ⋮ Quasi-locality and property A ⋮ Uniform Roe algebras of uniformly locally finite metric spaces are rigid ⋮ Ideals of band-dominated operators

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• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
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• Property A and the operator norm localization property for discrete metric spaces
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• Hyperbolic groups have finite asymptotic dimension
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