Quotient normed cones

Details Quotient normed cones Quotient normed cones

2006-07-25

arxiv.org/abs/math/0607619v1

Mathematics

Functional Analysis

17 pages

Scientific paper

Given a normed cone $(X,p)$ and a subcone $Y,$ we construct and study the quotient normed cone $(X/Y,\tilde{p})$ generated by $Y$. In particular we characterize the bicompleteness of $(X/Y,\tilde{p})$ in terms of the bicompleteness of $(X,p),$ and prove that the dual quotient cone $((X/Y)^{*},\|\cdot \|_{\tilde{p},u})$ can be identified as a distinguished subcone of the dual cone $(X^{*},\|\cdot \|_{p,u})$. Furthermore, some parts of the theory are presented in the general setting of the space $CL(X,Y)$ of all continuous linear mappings from a normed cone $(X,p)$ to a normed cone $(Y,q),$ extending several well-known results related to open continuous linear mappings between normed linear spaces.

Affiliated with

Also associated with

No associations

Rating

Quotient normed cones 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 Quotient normed cones, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quotient normed cones will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-666105