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 e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.04530
- arXiv:
- arXiv:2012.04530
- Bibcode:
- 2020arXiv201204530N
- Keywords:
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- Mathematics - Functional Analysis;
- 90C33;
- 15A18
- E-Print:
- 15 pages. arXiv admin note: text overlap with arXiv:2005.10508