Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

$M$-Local type conditions for the $C^*$-crossed product and local trajectories (2307.07019v2)

Published 13 Jul 2023 in math.OA

Abstract: The local trajectories method establishes invertibility in algebras $\mathcal{B}= \alg(\mathcal{A}, U_G)$, for a unital $C*$-algebra $\mathcal{A}$ with a non-trivial center, and a unitary group $U_g$, $g\in G$, with $G$ a discrete group, assuming that $G$ is amenable and the action $a\mapsto U_gaU_g*$ is topologically free. It is applicable in particular to $C*$-algebras associated with convolution type operators with amenable groups of shifts. We introduce here an $M$-local type condition that allows to establish an isomorphism between $\cB$ and a $C*$-crossed product, which is fundamental for the local trajectories method to work. We replace amenability of $G$ by the more general condition that action is amenable. The influence of the structure of the fixed points of the group action is analysed and a condition is introduced that applies when the action is not topologically free. If $\mathcal{A}$ is commutative, the referred conditions are related to the subalgebra $\alg(U_G)$ yielding, in particular, a sufficient condition that depends essentially on $U_G$. It is shown that in $\pi(\mathcal{B})= \alg(\pi(\mathcal{A}), \pi(U_G))$, with $\pi$ the local trajectories representation, the $M$-local type condition is verified, which allows establishing the isomorphism essential for the local trajectories method.

Summary

We haven't generated a summary for this paper yet.