Relative boundedness and relative compactness for linear operators in Banach spaces

被引：7

作者：

Binding, P ^{[1
]}

Hryniv, R

机构：

[1] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada

[2] Inst Appl Problems Mech & Math, UA-290601 Lviv, Ukraine

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 08期

关键词：

relatively bounded operators; relatively compact operators;

D O I：

10.1090/S0002-9939-00-05729-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If A and B are linear operators acting between Banach spaces, we show that compactness of B relative to A does not in general imply that B has A-bound zero. We do, however, give conditions under which the above implication is valid.

引用

页码：2287 / 2290

页数：4

共 50 条

[1] Relative compactness of orbits and geometry of Banach spaces
Farkas, Balint
Kreidler, Henrik
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 495 (01)
[2] THE COMPACTNESS AND THE RELATIVE POSITION IN BANACH-SPACES
CASTELLON, FG
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1991, 312 (11): : 769 - 772
[3] Relative boundedness in non-Archimedean Banach spaces
Ammar, Aymen
[J]. FILOMAT, 2023, 37 (29) : 9791 - 9821
[4] Perturbation of unbounded linear operators by γ-relative boundedness
Ammar, Aymen
Bouzayeni, Faten
Jeribi, Aref
[J]. RICERCHE DI MATEMATICA, 2018, 67 (02) : 433 - 445
[5] Relative boundedness and compactness theory for second-order differential operators
Anderson, TG
Hinton, DB
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 1997, 1 (04) : 375 - 400
[6] RELATIVE POSITION, SEQUENCES AND OPERATORS IN BANACH-SPACES
GARCIACASTELLON, F
[J]. MATHEMATISCHE NACHRICHTEN, 1994, 166 : 135 - 139
[7] Relative linear compactness
Xin, L
[J]. ALGEBRA COLLOQUIUM, 1998, 5 (01) : 67 - 75
[8] ON RELATIVE COMPACTNESS OF A SET OF ABSTRACT FUNCTIONS IN A SCALE OF BANACH-SPACES
PODGAEV, AG
[J]. SIBERIAN MATHEMATICAL JOURNAL, 1993, 34 (02) : 320 - 329
[9] BOUNDEDNESS AND COMPACTNESS OF HAUSDORFF OPERATORS ON FOCK SPACES
Blasco, Oscar
Galbis, Antonio
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024,
[10] On relative boundedness in operator spaces
Chebotarev, A
Liebscher, V
[J]. REPORTS ON MATHEMATICAL PHYSICS, 1999, 44 (03) : 339 - 344

← 1 2 3 4 5 →