Rank-one perturbations of diagonal operators

DOI10.1007/BF01203323zbMath0979.47012MaRDI QIDQ5937210

Eugen J. Ionascu

Publication date: 12 July 2001

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

zbMATH Keywords

eigenvaluesdiagonal Hilbert space operatorsinvariant subspace problemnormal operatorsone-codimension compressionsrank-one perturbationsselfadjoint compact operators

Mathematics Subject Classification ID

Linear operators defined by compactness properties (47B07) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Perturbation theory of linear operators (47A55) Invariant subspaces of linear operators (47A15) Dirichlet series, exponential series and other series in one complex variable (30B50)

Related Items (19)

Finite rank perturbations of normal operators: spectral subspaces and Borel series ⋮ Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators ⋮ Hyponormality of finite rank perturbations of normal operators ⋮ Halmos problems and related results in the theory of invariant subspaces ⋮ The geometry of spectral interlacing ⋮ Spectral decomposability of rank-one perturbations of normal operators ⋮ Cauchy-de Branges spaces, geometry of their reproducing kernels and multiplication operators ⋮ Finite rank perturbations of normal operators: spectral idempotents and decomposability ⋮ Rank one perturbations of diagonal operators without eigenvalues ⋮ Gaps of operators via rank-one perturbations ⋮ Reducing subspaces for rank-one perturbations of normal operators ⋮ Weighted join operators on directed trees ⋮ Resolvent algebra of finite rank operators ⋮ On rank-one perturbations of normal operators ⋮ Algebraic reflexivity of isometry groups and automorphism groups of some operator structures ⋮ Spectral analysis for finite rank perturbations of diagonal operators in non-Archimedean Hilbert space ⋮ Mirror operator and its application on chaos ⋮ Left-invertibility of rank-one perturbations ⋮ Weighted shifts on directed trees

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