Quasi-diagonality and the finite section method

DOI10.1090/S0025-5718-06-01893-XzbMath1113.65057arXivmath/0312316MaRDI QIDQ3420435

Nathanial P. Brown

Publication date: 2 February 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0312316

zbMATH Keywords

convergence analysisconvergenceGalerkin methodHilbert spacelinear operator equationsfinite section methodquasi-diagonal operatorquasi-diagonal operators

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Applications of functional analysis in numerical analysis (46N40)

Related Items (13)

Infinite-dimensional features of matrices and pseudospectra ⋮ Amenability of coarse spaces and \(\mathbb {K}\)-algebras ⋮ On spectral approximation, Følner sequences and crossed products ⋮ Finite section method in a space with two norms ⋮ Amenable traces and Følner \(C^\ast\)-algebras ⋮ The foundations of spectral computations via the solvability complexity index hierarchy ⋮ On the approximation of spectra of linear operators on Hilbert spaces ⋮ Computing spectral measures and spectral types ⋮ Convergence analysis of the finite section method and Banach algebras of matrices ⋮ Pseudoergodic operators and periodic boundary conditions ⋮ On the Solvability Complexity Index, the 𝑛-pseudospectrum and approximations of spectra of operators ⋮ On the infinite-dimensional QR algorithm ⋮ A note on commutation relations and finite dimensional approximations

Uses Software

• Pseudospectra

Cites Work

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• An exotic quasidiagonal operator
• Quasidiagonal weighted shifts
• On the approximation of quasidiagonal \(C^*\)-algebras
• Around quasidiagonal operators
• Invariant means and finite representation theory of 𝐶*-algebras
• Quasidiagonality of Direct Sums of Weighted Shifts
• AF Embeddings and the Numerical Computation of Spectra in Irrational Rotation Algebras
• Ten problems in Hilbert space
• An Extension of the Weyl-Von Neumann Theorem to Normal Operators
• \(C^*\)-algebras by example
• Herrero's approximation problem for quasidiagonal operators

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