Covariant representations of subproduct systems

Details Covariant representations of subproduct systems Covariant representations of subproduct systems

2010-04-18

arxiv.org/abs/1004.3004v2

Proc. Lond. Math. Soc. (3) 102, no. 4 (2011), 767-800

Mathematics

Operator Algebras

43 pages. Incorporates a few minor revisions, suggested by the referee and others

Scientific paper

10.1112/plms/pdq047

A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with finding conditions for a covariant representation of a \emph{subproduct system} to extend to a $C^*$-representation of the Toeplitz algebra. This framework is much more general than the former. We are able to find sufficient conditions, and show that in important special cases, they are also necessary. Further results include the universality of the tensor algebra, dilations of completely contractive covariant representations, Wold decompositions and von Neumann inequalities.

Affiliated with

Also associated with

No associations

Rating

Covariant representations of subproduct 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 Covariant representations of subproduct systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Covariant representations of subproduct systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-376620