Automatic Continuity of $ \ast $-Representations for Discrete Twisted $ C^{\ast} $-Dynamical Systems

TL;DR

This paper proves that all *-representations of discrete twisted C*-dynamical systems are automatically contractive in the L^1-norm, revealing a previously unknown property of these mathematical structures.

Contribution

It establishes the novel result that *-representations for discrete twisted C*-dynamical systems are inherently contractive in the L^1-norm, a significant theoretical insight.

Findings

All *-representations are automatically contractive in L^1-norm.

The result applies to discrete twisted C*-dynamical systems.

Provides new understanding of the structure of *-representations.

Abstract

In this paper, we will establish the relatively unknown result that every $ \ast $-representation for a discrete twisted $ C^{\ast} $-dynamical system $ (G,A,\alpha,\omega) $ is automatically contractive with respect to the $ L^{1} $-norm on $ {C_{c}}(G,A) $.