Let K be a convex subset of a Banach space X. In this paper we consider a class of nonexpansive maps <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_405_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="TEX">$T:K\rightarrow K$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>:</mo> <mi>K</mi> <mo stretchy="false">→</mo> <mi>K</mi> </mrow> </math></EquationSource> </InlineEquation> called <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_405_Article_IEq5.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathfrak {cm}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">cm</mi> </math></EquationSource> </InlineEquation>-nonexpansive. Our main result is a theorem that connects fixed point property (FPP), <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_405_Article_IEq5.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathfrak {cm}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">cm</mi> </math></EquationSource> </InlineEquation>-nonexpansiveness, <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_405_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\ell _1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> spreading models and Schauder bases with not-so-large projection constants. As a consequence, we deduce that Banach spaces with the weak Banach-Saks property have the FPP for <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_405_Article_IEq5.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathfrak {cm}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">cm</mi> </math></EquationSource> </InlineEquation>-nonexpansive maps.

$\ell _1$ spreading models and the FPP for Cesàro mean nonexpansive maps

期刊论文
发表日期：

2025年1月30日

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C. S. Barroso

摘要

Let K be a convex subset of a Banach space X. In this paper we consider a class of nonexpansive maps $T:K\rightarrow K$ $T : K \to K$ called $\mathfrak {cm}$ $cm$ -nonexpansive. Our main result is a theorem that connects fixed point property (FPP), $\mathfrak {cm}$ $cm$ -nonexpansiveness, $\ell _1$ $ℓ_{1}$ spreading models and Schauder bases with not-so-large projection constants. As a consequence, we deduce that Banach spaces with the weak Banach-Saks property have the FPP for $\mathfrak {cm}$ $cm$ -nonexpansive maps.

\(\ell _1\) spreading models and the FPP for Cesàro mean nonexpansive maps

摘要