Mutually polar retractions on convex cones

2020/12/08 by A. B. Németh, Németh, A. B. · 1 citation
Engineering · Mathematics · #15A18 #90C33 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematics and Applications #graph theory and CDMA systems #math.FA #msc:15A18 #msc:90C33

paper · pdf · doi:10.48550/arxiv.2012.04530

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

arxiv created 2020/12/08 · openalex publication_date 2020/12/08 · arxiv updated 2020/12/09 · openalex created_date 2020/12/21 · openalex updated_date 2026/07/28

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.

Citations

• Subadditive retractions on cones and asymmetric vector norms

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