New examples of [formula omitted]-saturated Banach spaces II

Abstract

For every Banach space Z with a shrinking unconditional basis satisfying an upper p-estimate for some p > 1 , an isomorphically polyhedral Banach space is constructed which has an unconditional basis and admits a quotient isomorphic to Z. It follows that reflexive Banach spaces with an unconditional basis and non-trivial type, Tsirelson's original space and ( ∑ c 0 ) ℓ p for p ∈ ( 1 , ∞ ) , are isomorphic to quotients of isomorphically polyhedral Banach spaces with unconditional bases.