Convergence analysis of the finite section method and Banach algebras of matrices

DOI10.1007/s00020-010-1775-xzbMath1197.65053OpenAlexW2056323326MaRDI QIDQ989599

Ziemowit Rzeszotnik, Thomas Strohmer, Karlheinz Gröchening

Publication date: 23 August 2010

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-010-1775-x

zbMATH Keywords

stabilityconvergenceBanach algebraslinear operator equationssystem of linear equationsfinite section methodinfinite systemBanach space of sequences

Mathematics Subject Classification ID

Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50)

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Cites Work

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• The inclusion of the Schur algebra in \(B(\ell^2)\) is not inverse-closed
• Propriétés des matrices ``bien localisées près de leur diagonale et quelques applications. (Properties of matrices ``well localized near the diagonal and some applications)
• A noncommutative Taylor formula and functions of triangle operators
• Time-frequency analysis of Sjöstrand's class
• Convergence analysis of the finite section method and Banach algebras of matrices
• Banach algebras of pseudodifferential operators and their almost diagonalization
• The band method for positive and strictly contractive extension problems: An alternative version and new applications
• Introduction to large truncated Toeplitz matrices
• \(C^*\)-algebras and numerical linear algebra
• Four short stories about Toeplitz matrix calculations
• Fredholm theory and finite section method for band-dominated operators
• Limit operators and their applications in operator theory
• Rates of convergence for the approximation of dual shift-invariant systems in \(\ell^2 (\mathbb{Z})\)
• Pseudodifferential operators and Banach algebras in mobile communications
• The finite section method for TOEPLITZ operators on the quarter-plane with piecewise continuous symbols
• Symmetry and inverse-closedness of matrix algebras and functional calculus for infinite matrices
• Quasi-diagonality and the finite section method
• Wiener’s lemma for infinite matrices
• Estimates for the entries of inverse matrices and the spectral analysis of linear operators
• Wiener’s lemma for twisted convolution and Gabor frames
• Algebras of approximation sequences: Finite sections of band-dominated operators
• Approximation of dual Gabor frames, window decay, and wireless communications