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<p>This paper introduces new absolute series spaces defined as the domain of a transformation matrix derived from the the <i>q</i>- Cesàro matrix on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _s\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell _{\infty }\)</EquationSource> </InlineEquation>. Their algebraic and topological constructions such as <i>BK</i>-space, isomorphism, duals and Schauder basis are investigated. In addition, some inclusion relations are examined. Then, some characterizations of compact and matrix operators on these spaces are obtained and their norms and Hausdorff measure of non-compactness are determined.</p>

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New Absolute q- Cesàro Series Spaces and Their Associated Matrix Transformations

  • 期刊论文

  • 发表日期：

    2025年9月18日

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  • Fadime Gökçe

摘要

This paper introduces new absolute series spaces defined as the domain of a transformation matrix derived from the the q- Cesàro matrix on \(\ell _s\) and \(\ell _{\infty }\) . Their algebraic and topological constructions such as BK-space, isomorphism, duals and Schauder basis are investigated. In addition, some inclusion relations are examined. Then, some characterizations of compact and matrix operators on these spaces are obtained and their norms and Hausdorff measure of non-compactness are determined.