Scholarlink

<p>We prove Grothendieck–Pietsch composition results for multiple summing operators without a linear analogue. As application, we give a new proof for the multilinear version of Grothendieck’s composition theorem proven by D. P érez-García and I. Villanueva. We use this result in tandem with the Maurey factorization theorem, to find the necessary and sufficient conditions for multilinear multiplication operator from a product of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(l_{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> spaces into <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(l_{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> to be multiple 2-summing.</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

Grothendieck–Pietsch composition results for multiple summing operators

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月3日

查看全文
  • Dumitru Popa

摘要

We prove Grothendieck–Pietsch composition results for multiple summing operators without a linear analogue. As application, we give a new proof for the multilinear version of Grothendieck’s composition theorem proven by D. P érez-García and I. Villanueva. We use this result in tandem with the Maurey factorization theorem, to find the necessary and sufficient conditions for multilinear multiplication operator from a product of \(l_{p}\) l p spaces into \(l_{1}\) l 1 to be multiple 2-summing.