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Abstract <p>In this article, we introduce greedy-type frame systems in Hilbert spaces. Some modified variants of greedy type frame systems, like super disjoint democratic and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(K\)</EquationSource> <!--ContMath2570024Yadav-m1--> </InlineEquation>-partially democratic, are introduced, and their existence and interrelationships are established. Also, frame systems satisfying different greedy-type properties specifically Property(<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(A\)</EquationSource> <!--ContMath2570024Yadav-m2--> </InlineEquation>), Property(<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(Q\)</EquationSource> <!--ContMath2570024Yadav-m3--> </InlineEquation>), Property (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Q^{*}\)</EquationSource> <!--ContMath2570024Yadav-m4--> </InlineEquation>) and Property (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(Q^{**}\)</EquationSource> <!--ContMath2570024Yadav-m5--> </InlineEquation>) are defined, and relations among them are established. Further, partially and consecutive almost greedy frame systems are defined, and new results are given. Additionally, examples highlight the contrasts between infinite and finite dimensional settings, providing insights into the structure and behavior of greedy frames.</p>

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On Greedy Types Frame Systems

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • U. Yadav,
  • R. Sharma,
  • S. Jahan

摘要

Abstract

In this article, we introduce greedy-type frame systems in Hilbert spaces. Some modified variants of greedy type frame systems, like super disjoint democratic and \(K\) -partially democratic, are introduced, and their existence and interrelationships are established. Also, frame systems satisfying different greedy-type properties specifically Property( \(A\) ), Property( \(Q\) ), Property ( \(Q^{*}\) ) and Property ( \(Q^{**}\) ) are defined, and relations among them are established. Further, partially and consecutive almost greedy frame systems are defined, and new results are given. Additionally, examples highlight the contrasts between infinite and finite dimensional settings, providing insights into the structure and behavior of greedy frames.