New examples of $c_0$-saturated Banach spaces II

TL;DR

This paper constructs a new class of Banach spaces with specific structural properties, including being isomorphically polyhedral and having quotients isomorphic to a broad class of spaces with unconditional bases.

Contribution

It introduces a method to build isomorphically polyhedral Banach spaces with unconditional bases that can produce quotients isomorphic to given spaces with certain basis and estimate properties.

Findings

Constructed Banach spaces are isomorphically polyhedral.

These spaces have unconditional bases.

They admit quotients isomorphic to a wide class of spaces with unconditional bases.

Abstract

For every Banach space $Z$ with a shrinking unconditional basis satisfying upper $p$-estimates for some $p > 1$, an isomorphically polyhedral Banach space is constructed having an unconditional basis and admitting a quotient isomorphic to $Z$.