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AIMS Mathematics

2024, Volume 9, Issue 9: 24193-24212. doi: 10.3934/math.20241177
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Research article

Compact operators on the new Motzkin sequence spaces

  • Department of Basic Engineering Sciences, Malatya Turgut Özal University, Malatya, Turkey
  • Received: 12 June 2024 Revised: 21 July 2024 Accepted: 26 July 2024 Published: 15 August 2024

  • MSC : 11B83, 46A45, 46B45, 47B07, 47B37

  • 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.

    Citation: Sezer Erdem. Compact operators on the new Motzkin sequence spaces[J]. AIMS Mathematics, 2024, 9(9): 24193-24212. doi: 10.3934/math.20241177

    Related Papers:

  • 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.



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