In this paper, we establish the lower bounds for the weakly convergent sequence coefficient <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1165_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="66" /> </InlineMediaObject> <EquationSource Format="TEX">$\text {WCS}(X)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>WCS</mtext> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of a Banach space X, in terms of the family of geometric constants <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1165_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">$C_{\lambda ,p}(X)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>C</mi> <mrow> <mi>λ</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, the coefficient of weak orthogonality <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1165_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$\mu (X)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, and the generalized García-Falset coefficient R(1, X). By means of these bounds, we identify some geometrical properties implying normal structure. Moreover, some sufficient conditions which imply uniform normal structure are presented. Our results significantly generalize and improve many known results in the literature.

On a general class of geometric constants and normal structure in Banach spaces

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发表日期：

2025年2月6日

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Mina Dinarvand

摘要

In this paper, we establish the lower bounds for the weakly convergent sequence coefficient $\text {WCS}(X)$ $WCS (X)$ of a Banach space X, in terms of the family of geometric constants $C_{\lambda ,p}(X)$ $C_{λ, p} (X)$ , the coefficient of weak orthogonality $\mu (X)$ $μ (X)$ , and the generalized García-Falset coefficient R(1, X). By means of these bounds, we identify some geometrical properties implying normal structure. Moreover, some sufficient conditions which imply uniform normal structure are presented. Our results significantly generalize and improve many known results in the literature.