Numerical range and functional calculus in Hilbert space

DOI10.1016/j.jfa.2006.10.013zbMath1116.47004OpenAlexW2005916081MaRDI QIDQ880112

Publication date: 10 May 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.10.013

zbMATH Keywords

numerical range completely bounded map spectral set functional calculus

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60) Numerical range, numerical radius (47A12) Spectral sets of linear operators (47A25)

Related Items

Stability of Runge-Kutta-Nyström methods, Variational analysis of the Crouzeix ratio, A Kreiss type inequality for rational functions on general domains, Rational Krylov methods for fractional diffusion problems on graphs, Spectral sets, extremal functions and exceptional matrices, Solving Rank-Structured Sylvester and Lyapunov Equations, Resolvent characterisation of generators of cosine functions and $C_0$-groups, Decomposing numerical ranges along with spectral sets, A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions, Solutions to operator equations on Hilbert $C^*$-modules. II, On the uniqueness of functions that maximize the Crouzeix ratio, On rational Krylov and reduced basis methods for fractional diffusion, Error Bounds for the Krylov Subspace Methods for Computations of Matrix Exponentials, The Numerical Range is a $(1+\sqrt{2})$-Spectral Set, Nonlinear acceleration of momentum and primal-dual algorithms, Between the von Neumann inequality and the Crouzeix conjecture, Crouzeix's conjecture and perturbed Jordan blocks, Joint numerical ranges: recent advances and applications minicourse by V. Müller and Yu. Tomilov, A proof of Crouzeix's conjecture for a class of matrices, Remarks on the Crouzeix--Palencia Proof that the Numerical Range is a (1+\sqrt2)-Spectral Set, Crouzeix's Conjecture Holds for Tridiagonal 3 x 3 Matrices with Elliptic Numerical Range Centered at an Eigenvalue, Convergence analysis of the extended Krylov subspace method for the Lyapunov equation, Localization in Matrix Computations: Theory and Applications, Convergence rates for Kaczmarz-type regularization methods, Low-Rank Updates of Matrix Functions, Numerical range and compressions of the shift, Crouzeix's conjecture and related problems, Lemniscates and $K$-spectral sets, Dilation theory: a guided tour, Arnoldi Algorithms with Structured Orthogonalization, Some Extensions of the Crouzeix--Palencia Result, Path-Following Method to Determine the Field of Values of a Matrix with High Accuracy, Krylov iterative methods for the geometric mean of two matrices times a vector, Decay properties for functions of matrices over $C^\ast$-algebras, Upper and lower bounds on norms of functions of matrices, The stability of rational approximations of cosine functions on Hilbert spaces, Preconditioning linear systems via matrix function evaluation, Numerical investigation of Crouzeix's conjecture, $H^{\infty}$ functional calculus and square function estimates for Ritt operators, The numerical range and the spectrum of a product of two orthogonal projections, Some uses of the field of values in numerical analysis, An Arnoldi-extrapolation algorithm for computing pagerank, Scaled and Squared Subdiagonal Padé Approximation for the Matrix Exponential, A functional calculus based on the numerical range: applications, Some Constants Related to Numerical Ranges, Approximating the leading singular triplets of a large matrix function, Decay bounds for the numerical quasiseparable preservation in matrix functions, Characterization of half-radial matrices, On mapping theorems for numerical range, A modified Gautschi's method without order reduction when integrating boundary value nonlinear wave problems, A new investigation of the extended Krylov subspace method for matrix function evaluations, Near Normal Dilations of Nonnormal Matrices and Linear Operators, Dilation theory in finite dimensions and matrix convexity, Shift-invert rational Krylov method for an operator $\phi $-function of an unbounded linear operator, A Note on Krylov Methods for Fractional Evolution Problems, Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture, Proxy-GMRES: Preconditioning via GMRES in Polynomial Space, Fast Singular Value Decay for Lyapunov Solutions with Nonnormal Coefficients, Complete spectral sets and numerical range, Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection, Convex domains and K-spectral sets, Ritt operators and convergence in the method of alternating projections, Tests for complete $K$-spectral sets

Cites Work