Applications of measure of noncompactness in operators on the spaces \(s_{\alpha}\), \(s_{\alpha}^{0}\), \(s_{\alpha}^{(c)}\), \(\ell_{\alpha}^{p}\) (Q852727)
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scientific article; zbMATH DE number 5072935
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Applications of measure of noncompactness in operators on the spaces \(s_{\alpha}\), \(s_{\alpha}^{0}\), \(s_{\alpha}^{(c)}\), \(\ell_{\alpha}^{p}\) |
scientific article; zbMATH DE number 5072935 |
Statements
Applications of measure of noncompactness in operators on the spaces \(s_{\alpha}\), \(s_{\alpha}^{0}\), \(s_{\alpha}^{(c)}\), \(\ell_{\alpha}^{p}\) (English)
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15 November 2006
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We characterize some operators and matrix transformations in the sequence spaces \(s_\alpha\), \(s^{(0)}_\alpha\), \(s^{(c)}_\alpha\), \(l^p_\alpha\). Moreover, using the Hausdorff measure of noncompactness, necessary and sufficient conditions are formulated for a linear operator between the mentioned spaces to be compact. Among other things, some results of \textit{L. W. Cohen} and \textit{N.~Dunford} [Duke Math.\ J.\ 3, 689--701 (1937; Zbl 0018.07101; JFM 63.0352.01)] are recovered.
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measure of noncompactness
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matrix transformation
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sequence space
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