Norm-closed intervals of norm-complete ordered abelian groups

Details Norm-closed intervals of norm-complete ordered abelian groups Norm-closed intervals of norm-complete ordered abelian groups

2005-01-25

arxiv.org/abs/math/0501460v1

Positivity 1 (1997) 271--290

Mathematics

General Mathematics

Scientific paper

Let $(G,u)$ be an archimedean norm-complete dimension group with order unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of $G$ which are closed with respect to the canonical norm of $(G,u)$. In particular, we establish a canonical one-to-one correspondence between closed intervals of $G$ and certain affine lower semicontinuous functions on the state space of $(G,u)$, which allows us to solve several problems of K. R. Goodearl about inserting affine continuous functions between convex upper semicontinuous and concave lower semicontinuous functions. This yields in turn new results about analogues of multiplier groups for norm-closed intervals.

Affiliated with

Also associated with

No associations

Rating

Norm-closed intervals of norm-complete ordered abelian groups 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 Norm-closed intervals of norm-complete ordered abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Norm-closed intervals of norm-complete ordered abelian groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-627836