Approximately inner derivations

Bratteli, Ola; Kishimoto, Akitaka; Robinson, Derek W.

Approximately inner derivations

Authors

Bratteli, Ola

Kishimoto, Akitaka

Robinson, Derek W.

Description

Let $α$ be an approximately inner flow on a $C^*$ algebra $A$ with generator $δ$ and let $δ_n$ denote the bounded generators of the approximating flows $α^{(n)}$. We analyze the structure of the set \cd=\{x\in D(δ): \lim_{n\to\infty}δ_n(x)=δ(x)\} of pointwise convergence of the generators. In particular we examine the relationship of $\cd$ and various cores related to spectral subspaces.
17 pages