On the Banach lattice c_0
Antonio Avil\'es, Gonzalo Mart\'inez-Cervantes, Jos\'e David, Rodr\'iguez Abell\'an
TL;DR
This paper investigates the projectivity of the Banach lattice c_0, showing it is not projective but is complemented in its free Banach lattice, leading to insights about the structure of free Banach lattices.
Contribution
It proves that c_0 is not a projective Banach lattice and that it is complemented in its free Banach lattice, clarifying the structure of free Banach lattices generated by c_0.
Findings
c_0 is not a projective Banach lattice
c_0 is complemented in its free Banach lattice
The free Banach lattice generated by c_0 is not projective
Abstract
We show that is not a projective Banach lattice, answering a question of B. de Pagter and A. Wickstead. On the other hand, we show that is complemented in the free Banach lattice generated by itself (seen as a Banach space). As a consequence, the free Banach lattice generated by is not projective.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topology and Set Theory · Advanced Algebra and Logic