Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The strong Nakano property in Banach lattices

Youssef Azouzi, Asma Ben Rjeb, Pedro Tradacete

Abstract

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 $c_0$ nor $L_1$.

The strong Nakano property in Banach lattices

Abstract

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 , the free Banach lattice has the strong Nakano property with a constant independent of the dimension. It is also shown that if has the strong Nakano property, then cannot contain subspaces isomorphic to neither nor .
Paper Structure (6 sections, 25 theorems, 75 equations)

This paper contains 6 sections, 25 theorems, 75 equations.

Table of Contents

  1. Introduction and preliminaries
  2. Basic facts
  3. Stability of the strong Nakano property
  4. Projections and the strong Nakano property
  5. Free Banach lattices and the strong Nakano property
  6. Strong Nakano of $FBL^{(p)}[\ell_1(A)]$

Key Result

Proposition 2.1

Let $X$ be an AM-space. $X$ has the strong Nakano property if and only if $X$ has a strong unit.

Theorems & Definitions (52)

  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • Corollary 2.3
  • Proposition 2.4
  • proof
  • Lemma 2.5
  • proof
  • Example 2.6
  • ...and 42 more