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Perturbation determinants in Banach spaces — with an application to eigenvalue estimates for perturbed operators
Author(s) -
Hansmann Marcel
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500315
Subject(s) - mathematics , eigenvalues and eigenvectors , banach space , perturbation (astronomy) , pure mathematics , linear operators , operator theory , mathematical analysis , physics , quantum mechanics , bounded function
In the first part of this paper we provide a self‐contained introduction to (regularized) perturbation determinants for operators in Banach spaces. In the second part, we use these determinants to derive new bounds on the discrete eigenvalues of compactly perturbed operators, broadly extending some recent results by Demuth et al. In addition, we also establish new bounds on the discrete eigenvalues of generators of C 0 ‐semigroups.