<p>It is shown that every <i>ε</i>-isometry of a convex body in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11253_2025_2408_Article_IEq3.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({l}_{\infty }^{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>l</mi> <mrow> <mi>∞</mi> </mrow> <mi>N</mi> </msubsup> </math></EquationSource> </InlineEquation> or in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11253_2025_2408_Article_IEq4.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({l}_{1}^{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> </math></EquationSource> </InlineEquation> can be well approximated by an affine surjective isometry.</p>

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ε-Isometries of Convex Bodies in \({l}_{\infty }^{N}\) And\({l}_{1}^{N}\)

  • Igor A.Vestfrid

摘要

It is shown that every ε-isometry of a convex body in \({l}_{\infty }^{N}\) l N or in \({l}_{1}^{N}\) l 1 N can be well approximated by an affine surjective isometry.