Positive operators on the n-dimensional ice cream cone

Abstract

Let Kn= {x ε{lunate} Rn: (x12 + · +x2n-1) 1 2 ≤ xn} be the n-dimensional ice cream cone, and let Γ(Kn) be the cone of all matrices in Rnn mapping Kn into itself. We determine the structure of Γ(Kn), and in particular characterize the extreme matrices in Γ(Kn). © 1975.