Approximately inner derivations

Abstract

Let $\alpha$ be an approximately inner flow on a $C^{\ast }$ algebra $A$ with generator $\delta$ and let ${\delta }_n$ denote the bounded generators of the approximating flows ${\alpha }^{(n)}$. 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