Abstract

On finite dimensional space, the spectral theorem provides the classification for normal operators. Similar results do hold for normal operators on infinite dimensional Hilbert space as well. However, beyond normal operators, very little is known. One of the many approaches is to study the operators by realizing them as part of so-called nice operators such as normal operators. This leads to the well known model theory introduced by Nagy-Foias and the theory of subnormal operators introduced by Halmos. The study of reproducing kernel Hilbert spaces. e.r. Hardy spaces, Bergman spaces, etc. and study of operators on them, e.g Toeplitz operators, Hankel operators, etc. came into prominence subsequently and applied successfully to various interpolation problems. Inequalities such as von Neumann inequality, Grothendieck inequality related these studies generated huge interest in the recent past. In this talk, we would try to give a glimpse of these studies in one and multi-variable setup and discuss some problems, if time permits.

About the Speaker

Dr. Shibananda Biswas is an Associate Professor in the Department of Mathematics and Statistics, IISER Kolkata.

Poster for the event, designed by Trishita Patra.