2019/05/16 by S. Z. Németh, Németh, S. Z.
Computer Science · Mathematics · #15A48 #90C33 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #math.OC #msc:15A48 #msc:90C33
paper · pdf · doi:10.48550/arxiv.1905.06885
arxiv created 2019/05/16 · openalex publication_date 2019/05/16 · arxiv updated 2019/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Z-property of a linear map with respect to a cone is an extension of the notion of Z-matrices. In a recent paper of Orlitzky (see Corollary 6.2 in M. Orlitzky. Positive and Z-operators on closed convex cones, Electron. J Linear Algebra, 444--458, 2018) the characterisation of cone-complementarity is given in terms of the dual of the cone of linear maps satisfying the Z-property. Therefore, it is meaningful to consider the problem of finding the dual cone of the cone of linear maps which have the Z-property with respect to a cone. This short note will solve this problem in the particular case when the Z-property is considered with respect to the Lorentz cone.