Recent progress on truncated Toeplitz operators

This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason's seminal paper in 2007.Comment: 46 page

Complex symmetric partial isometries

An operator T \in B(\h) is complex symmetric if there exists a conjugate-linear, isometric involution C:\h\to\h so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension $\leq 4$ is complex symmetric.Comment: 9 page

Model spaces: a survey

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.Comment: 55 page