Positive Operators on the n-Dimensional Ice-Cream Cone.

摘要

Let (K sub n) = (x epsilon (R sub n): ((x sub 1) squared + ... +(x sub (n-1)) squared) to the 1/2power =or < (x sub n) be the n-dimensional ice-cream cone,and let Gamma(K sub n) be the cone of all matrices in (R sup nn) mapping (K sub n) into itself. The authors determine the structure of Gamma(K sub n),and in particular characterize the extreme matrices in Gamma(K sub n). (Author)