Two-sided bounds and perturbation results for regularized determinants of infinite order compact operators
type: Item
instance of: scholarly article
title: Two-sided bounds and perturbation results for regularized determinants of infinite order compact operators
zbMATH Open document ID: 1151.47003
author: Michael I. Gil'
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-11-06T00:00:00Z
review text: A compact operator in a separable Hilbert space is called of infinite order if it does not belong to any Schatten-von Neumann ideal [cf. \textit{M. G. Kreĭn} and \textit{I. C. Gohberg}, ``Theory and applications of Volterra operators in Hilbert space'' (Translations of Mathematical Monographs 24, AMS, Providence/RI) (1970; Zbl 0194.43804)]. In the present paper, the author extends some results on determinants of Schatten-von Neumann operators to infinite order operators by presenting some upper and lower bounds for the regularized determinants of infinite order operators and gives some perturbation results.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A55
zbMATH DE Number: 5362169
zbMATH Keywords: compact linear operator
zbMATH Keywords: infinite order
zbMATH Keywords: regularized determinant
zbMATH Keywords: perturbations
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.09.001
OpenAlex ID: W1993429042
cites work: Schatten's theorems on functionally defined Schur algebras
cites work: Q5336643
cites work: Dyson's constant in the asymptotics of the Fredholm determinant of the sine kernel
cites work: Q4657624
cites work: Hankel operators in Schatten ideals
cites work: Q3622843
cites work: Traces and determinants of linear operators
cites work: Interpolation zwischen den Klassen 𝔖p von Operatoren in Hilberträumen
cites work: Q5590313
cites work: Higher order asymptotics of Toeplitz determinants with symbols in weighted Wiener algebras
cites work: Q4136031
cites work: An alternative to Plemelj-Smithies formulas on infinite determinants
cites work: Orlicz spaces and modular spaces
cites work: Q5801558
cites work: Q5694963
cites work: Q5699875
cites work: Intermittency and regularized Fredholm determinants
cites work: Determinant formula for the six-vertex model with reflecting end
cites work: Q4670861
cites work: On the Schatten class membership of Hankel operators on the unit ball
DOI: 10.1016/J.JMAA.2008.09.001
Recommended article: Perturbations of regularized determinants of operators in a Banach space
Recommended article: Regularized and L 2 -Determinants
Recommended article: On the regularized determinant for non-invertible elliptic operators
Recommended article: On the quotient of the regularized determinant of two elliptic operators
Recommended article: Q2958711
Recommended article: THE REGULARITY OF ORDER BOUNDED OPERATORS INTO C (K), II
Recommended article: Perturbation determinants in Banach spaces-with an application to eigenvalue estimates for perturbed operators
Recommended article: Q4382634
Recommended article: Q4006602
Recommended article: Regularized traces of a bounded perturbation of an operator with trace class resolvent
description: scientific article; zbMATH DE number 5362169