A note on the lattice properties of the linear maps of finite rank
John W. Chaney · Bulletin of the Australian Mathematical Society · 1973
It is shown that if E is a barreled locally convex lattice and F is a quasi-complete and order complete locally convex lattice then E′ ⊗ F equipped with the cone of positive continuous linear maps of finite rank is a lattice if and only if E′ or F has finite dimensional order intervals.