CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m |
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Authors: | Ivana Djolovic Eberhard Malkowsky |
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Affiliation: | a Technical Faculty, University of Belgrade, VJ 12, 19210 Bor, Serbia b Department of Mathematics, Faculty of Science, Fatih University, 34500 Büyükçekmece, Istanbul, Turkey |
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Abstract: | 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. |
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Keywords: | difference sequence spaces of order m matrix transformations compact operators Hausdorff measure of noncompactness |
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