This is an announcement for the paper “On the geometry of the Banach spaces $C([0, \alpha]\times K)$ for some scattered ♣-compacta” by Leandro Candidohttps://arxiv.org/find/math/1/au:+Candido_L/0/1/0/all/0/1.

Abstract: For some non-metrizable scattered $K$ compacta, constructed under the assumption of the Ostaszewski's ♣-principle, we study the geometry of the Banach spaces of the form $C(M\times K)$ where $M$ is a countable compact metric space. In particular, we classify up to isomorphism all the complemented subspaces of $C([0, \omega]\times K)$ and $C([0, \omega^{\omega}]\times K)$.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.01164