Mathematics – Operator Algebras
Scientific paper
2005-09-22
Mathematics
Operator Algebras
11 pages
Scientific paper
Let $A$ be a unital $C^*$-algebra and $\alpha$ be an injective, unital endomorphism of $A$. A covariant representation of $(A,\alpha)$ is a pair $(\pi,T)$ consisting of a $C^*$-representation $\pi$ of $A$ on a Hilbert space $H$ and a contraction $T$ in $B(H)$ satisfying $T\pi(\alpha(a))=\pi(a)T$. It follows from more general results of ours that such a covariant representation can be extended to a covariant representation $(\rho,V)$ (on a larger space $K$) such that $V$ is a coisometry and it can be dilated to a covariant representation $(\sigma,U)$ (on a larger space $K_1$) with $U$ unitary. Our objective here is to give self-contained, elementary proofs of these results which avoid the technology of $C^*$-correspondences. We also discuss the non uniqueness of the extension.
Muhly Paul S.
Solel Baruch
No associations
LandOfFree
Extensions and Dilations for $C^*$-dynamical Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Extensions and Dilations for $C^*$-dynamical Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extensions and Dilations for $C^*$-dynamical Systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-503583