Approximate determination of eigenvalues and eigenvectors of selfadjoint operators
We consider the problem of approximation of eigenvalues of a self-adjoint operator J defined by a Jacobi matrix in the Hilbert space l 2(ℕ) by eigenvalues of principal finite submatrices of an infinite Jacobi matrix that defines this operator. We assume the operator J is bounded from below with compact resolvent. In our research we estimate the asymptotics (with n → ∞) of the joint error of approximation for the eigenvalues, numbered from 1 to N; of J by the eigenvalues of the finite submatrix J...
The aim of the paper is twofold. First we give a survey of some recent results concerning the asymptotic behavior of the entropy and approximation numbers of compact Sobolev embeddings. Second we prove new estimates of approximation numbers of embeddings of weighted Besov spaces in the so called limiting case.
give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞
We consider an infinite Jacobi matrix with off-diagonal entries dominated by the diagonal entries going to infinity. The corresponding self-adjoint operator J has discrete spectrum and our purpose is to present results on the approximation of eigenvalues of J by eigenvalues of its finite submatrices.
Soient et . Il existe une application (non linéaire) normiquement continue de l’espace des opérateurs bornés de dans sur l’espace des opérateurs compacts (resp. faiblement compacts) de dans telle que coïncide avec la distance de au sous-espace formé des opérateurs compacts (resp. faiblement compacts). Pour un opérateur donné de dans on étudie les propriétés de l’ensemble (resp. ) des opérateurs compacts (resp. faiblement compacts) tel que pour tout de (resp. ) la quantité...
Given an operator ideal ℐ, a Banach space E has the ℐ-approximation property if the identity operator on E can be uniformly approximated on compact subsets of E by operators belonging to ℐ. In this paper the ℐ-approximation property is studied in projective tensor products, spaces of linear functionals, spaces of linear operators/homogeneous polynomials, spaces of holomorphic functions and their preduals.