On commutators of quadratic operators
Organizers
Speaker
Yuanhang Zhang
Time
Wednesday, March 27, 2024 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
A bounded linear operator $A$ is said to be quadratic if there is a polynomial $p$ of degree $2$ such that $p(A)=0$. Square zero operators, involutions, and idempotents are all typical quadratic operators.
We will give characterizations of matrices could be expressed as commutators of two square zero matrices, and explain some related results about limits of commutators of two square zero operators acting on a complex, separable Hilbert space $\mathcal{H}$.
We will also study the norm-closure of the set $\mathfrak{C}_{\mathfrak{E}}$ of bounded linear operators acting on $\mathcal{H}$ which may be expressed as the commutator of two idempotent operators. In particular, biquasitriangular operators belong to the norm-closure of $\mathfrak{C}_{\mathfrak{E}}$ are fully charateriezed.
This talk is based on joint papers with Laurent Marcoux and Heydar Radjavi.