This is an announcement for the paper "A weak*-topological dichotomy with applications in operator theory" by Tomasz Kania, Piotr Koszmider and Niels Jakob Laustsen. Abstract: Denote by $[0,\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on $[0,\omega_1)$ and vanish eventually. We show that a weakly$^*$ compact subset of the dual space of $C_0[0,\omega_1)$ is either uniformly Eberlein compact, or it contains a homeomorphic copy of the ordinal interval $[0,\omega_1]$. Using this result, we deduce that a Banach space which is a quotient of $C_0[0,\omega_1)$ can either be embedded in a Hilbert-generated Banach space, or it is isomorphic to the direct sum of $C_0[0,\omega_1)$ and a subspace of a Hilbert-generated Banach space. Moreover, we obtain a list of eight equivalent conditions describing the Loy--Willis ideal, which is the unique maximal ideal of the Banach algebra of bounded, linear operators on $C_0[0,\omega_1)$. As a consequence, we find that this ideal has a bounded left approximate identity, thus solving a problem left open by Loy and Willis, and we give new proofs, in some cases of stronger versions, of several known results about the Banach space $C_0[0,\omega_1)$ and the operators acting on it. Archive classification: math.FA math.GN Submitted from: t.kania@lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.0020 or http://arXiv.org/abs/1303.0020