A note on compact operators on matrix domains

被引：47

作者：

Djolovic, Ivana ^{[1
]}

Malkowsky, Eberhard ^{[2
,3
]}

机构：

[1] Univ Belgrade, Tech Fac, Bor 19210, Serbia

[2] Univ Giessen, Dept Math, D-35392 Giessen, Germany

[3] German Jordanian Univ, Sch Comp & Informat, Amman 11180, Jordan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 340卷 / 01期

关键词：

sequence spaces; BK and AK spaces; matrix domains; matrix transformations; compact operators; measure of noncompactness;

D O I：

10.1016/j.jmaa.2007.08.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish some identities or estimates for the operator norms and Hausdorff measures of noncompactness of linear operators given by infinite matrices that map the matrix domains of triangles in arbitrary BK spaces with AK, or in the spaces of all convergent or bounded sequences, into the spaces of all null, convergent or bounded sequences, or of all absolutely convergent series. Furthermore, we apply these results to the characterizations of compact operators on the matrix domains of triangles in the classical sequence spaces, and on the sequence spaces studied in [I. Djolovic, Compact operators on the spaces a(0)(r)(Delta) and a(c)(r)(Delta), J. Math. Anal. Appl. 318 (2) (2006) 658 - 666; 1. Djolovic, On the space of bounded Euler difference sequences and some classes of compact operators, Appl. Math. Comput. 182 (2) (2006) 1803 - 1811]. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：291 / 303

页数：13

共 19 条

[1] On the Euler sequence spaces which include the spaces lp and l∞I [J].