This is an announcement for the paper “Regular subspaces of a Bourgain-Delbaen space $\mathcal{B}_{mT}$” by Michał Świętekhttps://arxiv.org/find/math/1/au:+Swietek_M/0/1/0/all/0/1.
Abstract: The space $\mathcal{B}_{mt}[(m_j)_j, (n_j)_j]$ is a Bourgain-Delbaen space modelled on a mixed Tsirelson space $T[(m_j)_j, (n_j)_j]$ and is a slight modification of $\mathBB{B}_{mt}[(m_j)_j, (n_j)_j]$ a space defined by S. Argyros and R. Haydon. We prove that in every infinite dimensional subspace of $\mathcal{B}_{mt}[(m_j)_j, (n_j)_j]$ there exists a basic sequence equivalent to a sequence of weighted basis averages of increasing length from $T[(m_j)_j, (n_j)_j]$. We remark that the same is true for the original space $\mathBB{B}_{mt}[(m_j)_j, (n_j)_j]$.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.06481