The free Banach lattices generated by $$\ell _p$$ and $$c_0$$c0

Antonio Avilés,Pedro Tradacete,Ignacio Villanueva

The free Banach lattices generated by $$\ell _p$$ and $$c_0$$c0

2019

Antonio Avilés
Pedro Tradacete
Ignacio Villanueva

We prove that, when $2Banach lattice generated by \(\ell _p$ (respectively by $c_0$), the absolute values of the canonical basis form an $\ell _r$-sequence, where $\frac{1}{r} = \frac{1}{2} + \frac{1}{p}$ (respectively an $\ell _2$-sequence). In particular, in any Banach lattice, the absolute values of any $\ell _p$ sequence always have an upper $\ell _r$-estimate. Quite surprisingly, this implies that the free Banach lattices generated by the nonseparable $\ell _p(\Gamma )$ for \(2

Keywords:

Mathematical analysis
Free lattice
Lattice (order)
Topology
Banach lattice
Mathematics
Absolute value
Combinatorics
Standard basis

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