HAUSDORFF MEASURE OF NONCOMPACTNESS OF CERTAIN MATRIX OPERATORS ON ABSOLUTE NORLUND SPACES
HAUSDORFF MEASURE OF NONCOMPACTNESS OF CERTAIN MATRIX OPERATORS ON ABSOLUTE NORLUND SPACES
Summary: The absolute Nörlund spaces \(|N_p^u|_k\), \( k\geq 1\), have more recently been introduced and studied by \textit{G.~C. Hazar} and \textit{M.~A. Sarigöl} [Acta Math. Sin., Engl. Ser. 34, No.~5, 812--826 (2018; Zbl 1404.40005)]. In the present paper, we characterize the classes of infinite matrix and compact operators transforming from \(|N_p^u|_k\) into \(X\) and obtain some identities or estimates for the Hausdorff measures of noncompactness, where \(X\) is one of the spaces \(\ell_\infty\), \(c\) and \(c_0\).
- Pamukkale University Turkey
Transformations, absolute Nörlund spaces, Absolute Norlund spaces, Summability Factors, Absolute and strong summability, Sequence spaces, Functional analytic methods in summability, 510, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Matrix operators, Compact operators, Sequence-Spaces, Matrix methods for summability, BK spaces, sequence spaces, Banach sequence spaces, Sequence spaces (including Köthe sequence spaces), matrix operators, compact operators
Transformations, absolute Nörlund spaces, Absolute Norlund spaces, Summability Factors, Absolute and strong summability, Sequence spaces, Functional analytic methods in summability, 510, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Matrix operators, Compact operators, Sequence-Spaces, Matrix methods for summability, BK spaces, sequence spaces, Banach sequence spaces, Sequence spaces (including Köthe sequence spaces), matrix operators, compact operators
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