Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces
Copyright policy )Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces
We study the spacesw0p,wp, andw∞pof sequences that are strongly summable to 0, summable, and bounded with indexp≥1by the Cesàro method of order 1 and establish the representations of the general bounded linear operators from the spaceswpinto the spacesw∞1,w1, andw01. We also give estimates for the operator norm and the Hausdorff measure of noncompactness of such operators. Finally we apply our results to characterize the classes of compact bounded linear operators fromw0pandwpintow01andw1.
- Justus Liebig University Giessen Germany
- Fatih University Turkey
- King Abdulaziz University Saudi Arabia
spaces of strongly summable sequences, bounded linear operators, QA1-939, Linear operators defined by compactness properties, compactness, Norms (inequalities, more than one norm, etc.) of linear operators, Absolute and strong summability, Mathematics, Sequence spaces (including Köthe sequence spaces), Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
spaces of strongly summable sequences, bounded linear operators, QA1-939, Linear operators defined by compactness properties, compactness, Norms (inequalities, more than one norm, etc.) of linear operators, Absolute and strong summability, Mathematics, Sequence spaces (including Köthe sequence spaces), Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
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