On matrix transformations and Hausdorff measure of noncompactness of Euler difference sequence spaces of fractional order. (English) Zbl 07311143
Summary: In the present paper, some results on matrix mappings and Hausdorff measure of noncompactness of certain generalized Euler difference sequence spaces of fractional order are discussed. Also, the Hausdorff measures of noncompactness of certain matrix operators that map an arbitrary \(BK\)-space into the classical sequence spaces are established. Furthermore, by using this measure, the characterization of some classes of Euler mean compact operators are determined in the \(BK\)-spaces.
MSC:
| 47-XX | Operator theory |
| 46A45 | Sequence spaces (including Köthe sequence spaces) |
| 46B45 | Banach sequence spaces |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
Keywords:
difference operators \(\Delta^{(\overline{\alpha})}, \Delta^{(-\overline{\alpha})}\); Euler mean operator \(E^r\); \(BK\) spaces; bounded and compact linear operators; Hausdorff measure of noncompactnessReferences:
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