Vector spaces with an order unit

Details Vector spaces with an order unit Vector spaces with an order unit

2007-12-17

arxiv.org/abs/0712.2613v4

Mathematics

Operator Algebras

38 pages, uses XY-pic, Version 2 comments: minor typos corrected.; Version 3 Comments: minor typos corrected; Version 4 Commen

Scientific paper

We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple extensions to an order (semi)norm on the entire space. We single out three of these (semi)norms for further study and discuss their significance for operator algebras and operator systems. In addition, we introduce a functorial method for taking an ordered space with an order unit and forming an Archimedean ordered space. We then use this process to describe an appropriate notion of quotients in the category of Archimedean ordered spaces.

Affiliated with

Also associated with

No associations

Rating

Vector spaces with an order unit 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 Vector spaces with an order unit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vector spaces with an order unit will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-115659