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.

15 pages. arXiv admin note: text overlap with arXiv:2005.10508

References in corpus (1)

• Subadditive retractions on cones and asymmetric vector norms

Cited by in corpus (1)

• Geometry of the proper asymmetric norm