On linear preservers of semipositive matrices

2019/10/25 by Jayaraman, Sachindranath, Mer, Vatsalkumar N.
#15A86 #15B48 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1910.11532

Abstract

Given proper cones K₁ and K₂ in ℝⁿ and ℝ^m, respectively, an m × n matrix A with real entries is said to be semipositive if there exists a x ∈ K₁^∘ such that Ax ∈ K₂^∘, where K^∘ denotes the interior of a proper cone K. This set is denoted by S(K₁,K₂). We resolve a recent conjecture on the structure of into linear preservers of S(ℝⁿ₊,ℝ^m₊). We also determine linear preservers of the set S(K₁,K₂) for arbitrary proper cones K₁ and K₂. Preservers of the subclass of those elements of S(K₁,K₂) with a (K₂,K₁)-nonnegative left inverse as well as connections between strong linear preservers of S(K₁,K₂) with other linear preserver problems are considered.

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