Analysis Seminar: "Cyclicity preserving operators on reproducing kernel Hilbert spaces"

Speaker: Jeet Sampat, Washington University in Saint Louis

Abstract: We shall prove a Gleason-Kahane-Zelazko type theorem for spaces of analytic functions in several complex variables and use it to show that in a reasonable setting, operators that preserve shift cyclicity are going to be weighted composition operators. A natural question one can ask is “can such a result be proved for spaces of non-analytic functions?” In this talk, we will apply similar techniques for RKHS with a cyclic multiplication operator and prove that all operators that preserve cyclicity w.r.t. this multiplication operator are some form of a weighted composition operator as well.

Host: Brett Wick