Mutually polar retractions on convex cones
Abstract
Two retractions Q and R on closed convex cones M and respectively N of a Banach space are called mutually polar if Q+R=I and QR=RQ=0. This note investigates the existence of a pair of mutually polar retractions for given cones M and N. It is shown that if dim N=1 (or dim M=1) then the retractions are subadditive with respect to the order relation their cone range endow.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.04530
 arXiv:
 arXiv:2012.04530
 Bibcode:
 2020arXiv201204530N
 Keywords:

 Mathematics  Functional Analysis;
 90C33;
 15A18
 EPrint:
 15 pages. arXiv admin note: text overlap with arXiv:2005.10508