An Introduction to Toeplitz Operators and k-Hyponormality

Sam Holen

In this talk we will discuss some foundations in the theory of Toeplitz operators on the Hardy-Hilbert space of the unit circle. We will go over several results that will elucidate what makes these operators special. We then briefly introduce Hankel operators and their connection to Toeplitz operators, a fact we shall use in proving that a certain class of Toeplitz operators is subnormal. Also, to that end, we discuss at some length the notions of hyponormality, k-hyponormality, and progress that has been made in classifying which Toeplitz operators satisfy these properties.

To participate in this event virtually via Zoom, go to https://uiowa.zoom.us/j/95316149275.