Chain conditions in free Banach lattices
Antonio Avil\'es, Grzegorz Plebanek, Jos\'e David Rodr\'iguez, Abell\'an
TL;DR
This paper proves that the free Banach lattice generated by any Banach space satisfies the sigma-bounded chain condition, contributing to the understanding of chain conditions in Banach lattice theory.
Contribution
It establishes that all free Banach lattices generated by arbitrary Banach spaces satisfy the sigma-bounded chain condition, a new structural property.
Findings
FBL[E] satisfies the sigma-bounded chain condition for any Banach space E.
Provides insight into the chain conditions in free Banach lattices.
Advances the theoretical understanding of Banach lattice structures.
Abstract
We show that for an arbitrary Banach space , the free Banach lattice generated by satisfies the -bounded chain condition.
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