Compact operators on the new Motzkin sequence spaces

This study aims to construct the BK-spaces $ \ell_p(\mathcal{M}) $ and $ \ell_{\infty}(\mathcal{M}) $ as the domains of the conservative Motzkin matrix $ \mathcal{M} $ obtained by using Motzkin numbers. It investigates topological properties, obtains Schauder basis, and then gives inclusion relation...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 9; pp. 24193 - 24212
Main Author Erdem, Sezer
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
compact operators
hausdorff measure of non-compactness
matrix mappings
motzkin numbers
sequence spaces
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Summary:This study aims to construct the BK-spaces $ \ell_p(\mathcal{M}) $ and $ \ell_{\infty}(\mathcal{M}) $ as the domains of the conservative Motzkin matrix $ \mathcal{M} $ obtained by using Motzkin numbers. It investigates topological properties, obtains Schauder basis, and then gives inclusion relations. Additionally, it expresses $ \alpha $-, $ \beta $-, and $ \gamma $-duals of these spaces and submits the necessary and sufficient conditions of the matrix classes between the described spaces and the classical spaces. In the last part, the characterization of certain compact operators is given with the aid of the Hausdorff measure of non-compactness.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20241177