### $\sigma$-$C^*$-dynamics of $\mathcal{K}(H)$

#### Abstract

Let $\sigma$ be a linear $*$-endomorphism on a $C^*$-algebra $A$ so that $\sigma(A)$ acts on a Hilbert space $H$ which including $\mathcal{K}(H)$

and let $\{\alpha_t\}_{t\in\mathbb{R}}$ be a $\sigma$-$C^*$-dynamical system

on $A$ with the generator $\delta.$ In this paper, we

demonstrate some conditions under which $\{\alpha_t\}_{t\in\mathbb{R}}$ is implemented by a

$C_0$-groups of unitaries on $H$.

and let $\{\alpha_t\}_{t\in\mathbb{R}}$ be a $\sigma$-$C^*$-dynamical system

on $A$ with the generator $\delta.$ In this paper, we

demonstrate some conditions under which $\{\alpha_t\}_{t\in\mathbb{R}}$ is implemented by a

$C_0$-groups of unitaries on $H$.

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution 3.0 License.