Scholarlink

<p>We study the strong Nakano property in Banach lattices with a special focus on free Banach lattices. We show that for every finite dimensional Banach space <i>E</i>, the free Banach lattice <i>FBL</i>[<i>E</i>] has the strong Nakano property with a constant independent of the dimension. It is also shown that if <i>FBL</i>[<i>E</i>] has the strong Nakano property, then <i>E</i> cannot contain subspaces isomorphic to neither <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(c_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> nor <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>1</mn> </msub> </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

The strong Nakano property in Banach lattices

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月23日

查看全文
  • Youssef Azouzi,
  • Asma Ben Rjeb,
  • Pedro Tradacete

摘要

We study the strong Nakano property in Banach lattices with a special focus on free Banach lattices. We show that for every finite dimensional Banach space E, the free Banach lattice FBL[E] has the strong Nakano property with a constant independent of the dimension. It is also shown that if FBL[E] has the strong Nakano property, then E cannot contain subspaces isomorphic to neither \(c_0\) c 0 nor \(L_1\) L 1 .