Nilpotent elements of operator ideals as single commutators

On single commutators in II_1-factors

We investigate the question of whether all elements of trace zero in a II_1-factor are single commutators. We show that all nilpotent elements are single commutators, as are all normal elements of trace zero whose spectral distributions are discrete measures. Some other classes of examples are considered.

Sums of commutators in ideals and modules of type II factors

Let M be a factor of type II_\infty or II_1 having separable predual and let M-bar be the algebra of affiliated τ-measureable operators. We characterize the commutator space [I,J] for sub-(M,M)-bimodules I and J of M-bar.

Generalized Berezin Transform and Commutator Ideals

For a quasi-free module over a function algebra $A(Ω)$, we define an analogue of the Berezin transform and relate this to the quotient of the C*-algebra it generates modulo the commutator ideal.

由换位子生成的环与 C*-代数

Rings and C*-algebras generated by commutators

本文刻画含单位元环由换位子理想生成的条件，并给出矩阵环、真无限或实秩零及 Jiang-Su 稳定 C*-代数的统一乘积项数界。

环中完全非中心Lie理想与不变加法子群

Fully noncentral Lie ideals and invariant additive subgroups in rings

本文证明了环中完全非中心子群包含所有加法换位子的条件，并揭示了在特定代数中完全非中心子空间成为Lie理想与内自同构不变性的等价关系。

A survey on the interplay between arithmetic mean ideals, traces, lattices of operator ideals, and an infinite Schur-Horn majorization theorem

The work of Dykema, Figiel, Weiss, and Wodzicki on the structure of commutators showed that arithmetic means play an important role in the study of operator ideals, and we explored their role in a multipaper project which we survey in this article. We start by presenting the notions of arithmetic mean ideals and arithmetic mean at infinity ideals. Then we explore their connections with commutator spaces, traces, elementary operators, lattice and sublattice structure of ideals, arithmetic mean ideal cancellation properties of first and second order, and softness properties - a term that we intr…