Some spectral properties of positive linear operators
Helmut Schaefer · Pacific Journal of Mathematics · 1960
Based on research sponsored by the Office of Ordnance Research, U.S. Army.1 For the terminology adopted, see § 1.2 A short proof in [14].Cf. also [5]. 3 With only minor modifications, the results of the present paper carry over to bounded positive endomorphisms of a partially ordered, quasi-complete locally convex space.1009 4 i.e., a binary relation which is reflexive and transitive.We assume always that EΦ{0}.6 K is proper if and only if the order relation is anti-symmetric. S c E is symmetric if x£S implies -xGS.In the (present) case of a normed space, K is a Z?-cone if and only if there exists an m > 0 such that every x in the unit ball U of E is of the form x = lim w _»oo (u nv n ) with u n ,v n 6 K Π m U,