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The effect of finite rank perturbations on Jordan chains of linear operators

2014/03/30 by Jussi Behrndt, Leslie Leben, Behrndt, Jussi +5
Computer Science · Mathematics · #15A18 #47A10 #47A55 #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.FA #msc:15A18 #msc:47A10 #msc:47A55

paper · pdf · doi:10.48550/arxiv.1403.7758

openalex publication_date 2014/03/30 · arxiv created 2015/03/31 · arxiv updated 2015/04/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

A general result on the structure and dimension of the root subspaces of a matrix or a linear operator under finite rank perturbations is proved: The increase of dimension from the n-th power of the kernel of the perturbed operator to the (n+1)-th power differs from the increase of dimension of the corresponding powers of the kernels of the unperturbed operator by at most the rank of the perturbation and this bound is sharp.

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