北京雁栖湖应用数学研究院

黄林哲 , 刘正伟 , Sébastien Palcoux , 王亦龙 , 吴劲松

张远航

2024年03月27日 10:30 至 12:00

A3-3-301

Zoom 242 742 6089 (BIMSA)

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.