REGULARIZED TRACE FORMULA FOR DISCRETE OPERATORS WITH A PERTURBATION IN THE SCHATTEN-VON NEUMANN CLASS

被引：2

作者：

Murtazin, Kh. Kh. ^{[1
]}

Fazullin, Z. Yu. ^{[1
]}

机构：

[1] Bashkir State Univ, Zaki Validi Str 32, Ufa 450074, Russia

来源：

UFA MATHEMATICAL JOURNAL | 2015年 / 7卷 / 04期

关键词：

perturbation theory; regularized trace; discrete operator; spectrum; resolvent;

D O I：

10.13108/2015-7-4-104

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper we study a regularized trace formula for discrete self-adjoint operators with a perturbation in Schatten-von Neumann class (sigma(p), p is an element of N). We prove that the regularized trace vanishes after deducting (p - 1) terms of perturbation theory if there are no dilating gaps in the spectrum of the unperturbed operator.

引用

页码：104 / 110

页数：7

共 50 条

[21] Berezin symbols and Schatten-von Neumann classes
Karaev, MT
MATHEMATICAL NOTES, 2002, 72 (1-2) : 185 - 192
[22] Schatten-von Neumann properties in the Weyl calculus
Buzano, Ernesto
Toft, Joachim
JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (12) : 3080 - 3114
[23] On the lower bounds for Schatten-von Neumann norms of certain Volterra integral operators
Stepanov, VD
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2000, 61 : 905 - 922
[24] Toeplitz Operators with Radial Symbols on Bergman Space and Schatten-von Neumann Classes
Bendaoud, Z.
Kupin, S.
Toumache, K.
Toure, B.
Zarouf, R.
JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, 2020, 16 (01) : 3 - 26
[25] Bounds for eigenvalues of Schatten-von Neumann operators via self-commutators
Gil, Michael
JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 267 (09) : 3500 - 3506
[26] Schur multipliers in Schatten-von Neumann classes
Conde-Alonso, Jose M.
Gonzalez-Perez, Adrian M.
Parcet, Javier
Tablate, Eduardo
ANNALS OF MATHEMATICS, 2023, 198 (03) : 1229 - 1260
[27] The Schatten-von Neumann class associated with the Gabor-Riemann-Liouville operator
Hammami, Aymen
PERIODICA MATHEMATICA HUNGARICA, 2021, 83 (02) : 192 - 203
[28] ALMOST-ORTHOGONALITY IN THE SCHATTEN-VON NEUMANN CLASSES
Carbery, Anthony
JOURNAL OF OPERATOR THEORY, 2009, 62 (01) : 151 - 158
[29] Schur multipliers of Schatten-von Neumann classes Sp
Aleksandrov, A. B.
Peller, V. V.
JOURNAL OF FUNCTIONAL ANALYSIS, 2020, 279 (08)
[30] Triple operator integrals in Schatten-von Neumann norms and functions of perturbed noncommuting operators
Aleksandrov, Aleksei
Nazarov, Fedor
Peller, Vladimir
COMPTES RENDUS MATHEMATIQUE, 2015, 353 (08) : 723 - 728

← 1 2 3 4 5 →