This is an announcement for the paper “Subsymmetric weak$^*$ Schauder bases and factorization of the identity” by Richard Lechnerhttps://arxiv.org/find/math/1/au:+Lechner_R/0/1/0/all/0/1. Abstract: Let $X^*$ denote a Banach space with a subsymmetric weak$^*$ Schauder basis satisfying condition. We show that for any operator $T: X^*\rightarrow X^*$ either $T(X^*)$ or $(I-T)(X^*)$ contains a subspace that is isomorphic to $X^*$ and complemented in $X^*$. Moreover, we prove that $\ell_p(X^*), 1\leq p\leq\infty$ is primary.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1804.01372