Analysis Seminar: "Algebraic properties of m-isometries"
Speaker: Trieu Le, University of Toledo
Abstract: m-Isometries are Hilbert space linear operators satisfying an operator equation that generalizes the notion of isometries. These operators were introduced and studied by Agler. In the late nineties, Agler, Helton and Stankus showed that any m-isometry on a finite dimensional Hilbert space can be decomposed as a sum of an isometry and a commuting nilpotent operator. The converse of this and other algebraic properties of m-isometries have been proved in recent years. I will discuss how the hereditary functional calculus can be used to provide simplified proofs of these as well as more general results, even in the setting of commuting tuples of operators.
Host: Christopher Felder