<p>In this paper, we present two new geometric constants related to isosceles orthogonality <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1966_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">$M(X,\alpha ,\beta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1966_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="TEX">$M_2(X,\alpha ,\beta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, which are generalizations of the rectangular constant proposed by Joly. First, we give upper and lower bounds of these geometric constants. Then we characterize Hilbert spaces in terms of these constants. Furthermore, the relationship between these geometric constants and uniformly non-squareness is also discussed. Finally, we give a characterization of Radon planes with an affine regular hexagonal unit sphere by means of the constants <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1966_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">$M(X,\alpha ,\beta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1966_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="TEX">$M_2(X,\alpha ,\beta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

Generalized rectangular modulus related to isosceles orthogonality in Banach spaces

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发表日期：

2025年9月15日

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Huayou Xie,
Qi Liu,
Yongjin Li

摘要

In this paper, we present two new geometric constants related to isosceles orthogonality $M(X,\alpha ,\beta )$ $M (X, α, β)$ and $M_2(X,\alpha ,\beta )$ $M_{2} (X, α, β)$ , which are generalizations of the rectangular constant proposed by Joly. First, we give upper and lower bounds of these geometric constants. Then we characterize Hilbert spaces in terms of these constants. Furthermore, the relationship between these geometric constants and uniformly non-squareness is also discussed. Finally, we give a characterization of Radon planes with an affine regular hexagonal unit sphere by means of the constants $M(X,\alpha ,\beta )$ $M (X, α, β)$ and $M_2(X,\alpha ,\beta )$ $M_{2} (X, α, β)$ .