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On ๐‘›-widths in ๐ฟ^{โˆž}

On ๐‘›-widths in ๐ฟ^{โˆž}

The <italic>n</italic>-width in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript normal infinity"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi mathvariant="normal">โˆž<!-- โˆž --></mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{L^\infty }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of certain sets determined by matrices and integral operators is determined. The notion of total positivity is essential in the analysis.