Partially isometric Toeplitz operators on the polydisc
In this talk, we will discuss Toeplitz operators on the Hardy space over the polydisc. In particular, we are interested in the classification of partially isometric Toeplitz operators. Such a classification was first studied by A. Brown and R. G. Douglas, in the case of Hardy space over the disc, by exploiting the celebrated Beurling-Lax-Halmos(BLH) theorem. Though the absence of BLH-type result in higher dimensions presents an obvious obstruction, yet we will present a satisfactory and novel generalization of Brown-Douglas theorem. This talk is based on a joint work with Deepak K.D. and J. Sarkar.