A note on the commutator of two operators on a locally convex space

被引：0

作者：

Kramar, Edvard ^{[1
]}

机构：

[1] Univ Ljubljana, Fac Math & Phys, Jadranska 19, Ljubljana 1000, Slovenia

来源：

COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE | 2016年 / 57卷 / 02期

关键词：

locally convex space; commutator; nilpotent operator; compact operator; Riesz operator;

D O I：

10.14712/1213-7243.2015.155

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Denote by C the commutator AB - BA of two bounded operators A and B acting on a locally convex topological vector space. If AC - CA = 0, we show that C is a quasinilpotent operator and we prove that if AC - CA is a compact operator, then C is a Riesz operator.

引用

页码：163 / 168

页数：6

共 50 条

[1] A NOTE ON SEMIGROUPS OF OPERATORS ON A LOCALLY CONVEX SPACE
SINGBALVEDAK, K
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 16 (04) : 696 - +
[2] A Note on Supercyclic Operators in Locally Convex Spaces
Albanese, Angela A.
Jornet, David
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019, 16 (05)
[3] A Note on Supercyclic Operators in Locally Convex Spaces
Angela A. Albanese
David Jornet
Mediterranean Journal of Mathematics, 2019, 16
[4] REMARKS ON SPECTRA OF OPERATORS ON A LOCALLY CONVEX SPACE
MAEDA, F
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1961, 47 (07) : 1052 - &
[5] REGULAR SPECTRAL OPERATORS ON A LOCALLY CONVEX SPACE
BERRUYER, J
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1968, 267 (19): : 686 - &
[6] REGULAR DECOMPOSABLE OPERATORS ON A LOCALLY CONVEX SPACE
BERRUYER, J
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1969, 268 (26): : 1596 - &
[7] FUNDAMENTAL HYPERFUNCTIONS OF EVOLUTION OPERATORS IN A LOCALLY CONVEX SPACE
VUVUNIKIAN, IM
DOKLADY AKADEMII NAUK SSSR, 1977, 235 (05): : 1001 - 1004
[8] Holomorphic functional calculus for operators on a locally convex space
H. Arikan
L. Runov
V. Zahariuta
Results in Mathematics, 2003, 43 (1-2) : 23 - 36
[9] FUNDAMENTAL FUNCTIONS OF DIFFERENTIAL OPERATORS IN LOCALLY CONVEX SPACE
VAINERMAN, VI
VUVUNIKYAN, YM
DOKLADY AKADEMII NAUK SSSR, 1974, 214 (01): : 15 - 18
[10] A NOTE ON GENERATION OF NONLINEAR SEMIGROUPS IN A LOCALLY CONVEX SPACE
OHARU, S
PROCEEDINGS OF THE JAPAN ACADEMY, 1967, 43 (09): : 847 - &

← 1 2 3 4 5 →