New examples of $c_0$-saturated Banach spaces

TL;DR

This paper constructs new Banach spaces with specific properties, including unconditional bases and quotients isomorphic to 5p, and demonstrates their non-embeddability into certain function spaces, advancing the understanding of Banach space structures.

Contribution

It introduces a new class of 5p-saturated Banach spaces with unconditional bases and analyzes their embedding properties, which was not previously known.

Findings

Constructed 5p-saturated Banach spaces with unconditional bases.

Proved these spaces admit quotients isomorphic to 5p.

Showed these spaces cannot embed into any C(K) space for countable compact K.

Abstract

For every $ 1 < p < \infty $ an isomorphically polyhedral Banach space $E_p$ is constructed having an unconditional basis and admitting a quotient isomorphic to $\ell_p$. It is also shown that $E_p$ is not isomorphic to a subspace of a $C(K)$ space for every countable and compact metric space $K$.