半序线性空间的对偶定理

DUALITY THEOREMS IN ORDERED VECTOR SPACES

研究右序对偶半序线性空间中两个不同的Ｍａｃｋｅｙ邻域的对偶，给出一类对偶定理的一般形式，削弱了关于序凸与可分解，绝对序凸与绝对控及正序凸与正控的对偶定理的某些条件并简化了其证明．

Let (E,E +) and (F,F +) be partially ordered vector spaces which form an ordered duality on the right,the duality of two different τ(E,F)-neighborhood of 0 was studied,where τ(E,F) denotes the Mackey topology on E. A general form of a class of duality theorems was yielded. As corollaries some results were obtained on dualities of order-convex and decomposable,absolutely order-convex and absolutely dominated, and positively order-convex and positively dominated,but our assumptions were weaker and our proofs were more simple.