CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them....

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Bibliographic Details
Published in:Acta mathematica scientia 2011-07, Vol.31 (4), p.1465-1474
Main Authors: Djolovic, Ivana, Malkowsky, Eberhard
Format: Article
Language:English
Subjects:
46B15
46B45
46B50
compact operators
difference sequence spaces of order m
ERC
Hausdorff measure of noncompactness
Hausdorff测度
matrix transformations
Operators
Transformations
Triangles
三角矩阵
差分序列
序列空间
矩阵变换
紧算子
运营商
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Summary:In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(11)60332-9