Scholarlink

<p>A point <i>x</i> is a point of approximative compactness for a&#xa0;set&#xa0;<i>M</i> if any minimizing sequence from&#xa0;<i>M</i> for&#xa0;<i>x</i> contains a&#xa0;subsequence converging to some point from&#xa0;<i>M</i>. We obtain several characterizations for points of approximative compactness for special subsets (a&#xa0;closed ball, the complement of an open ball) in classical sequence spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(c_0(\Gamma )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(c(\Gamma )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\ell ^p(\Gamma )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(1\le p\le \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>p</mi> <mo>≤</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

APPROXIMATIVE COMPACTNESS IN CLASSICAL SEQUENCE SPACES

  • 期刊论文

  • 发表日期：

    2026年3月19日

查看全文
  • Hu Fang

摘要

A point x is a point of approximative compactness for a set M if any minimizing sequence from M for x contains a subsequence converging to some point from M. We obtain several characterizations for points of approximative compactness for special subsets (a closed ball, the complement of an open ball) in classical sequence spaces \(c_0(\Gamma )\) c 0 ( Γ ) , \(c(\Gamma )\) c ( Γ ) , \(\ell ^p(\Gamma )\) ℓ p ( Γ ) , \(1\le p\le \infty \) 1 ≤ p ≤ ∞ .