A new isomorphic (\ell_1) predual not isomorphic to a complemented subspace of a (C(K)) space

TL;DR

This paper constructs a new -predual space that cannot be embedded into any C(K) space nor is it isomorphic to a complemented subspace of one, revealing new structural limitations.

Contribution

It introduces a novel -predual space with unique embedding properties, not isomorphic to subspaces of c_0 or C(\u03c9^) spaces.

Findings

The constructed space is not isomorphic to a subspace of c_0.

The space is not isomorphic to a subspace of C(\u03c9^).

It is not isomorphic to a complemented subspace of any C(K) space.

Abstract

An isomorphic (\ell_1)-predual space (X) is constructed such that neither (X) is isomorphic to a subspace of (c_0), nor (C(\omega^\omega)) is isomorphic to a subspace of (X). It follows that (X) is not isomorphic to a complemented subspace of a (C(K)) space.