中文摘要：

众所周知,对于Banach空间X,l~1（X）的共轭空间可以表示为l~∞（X＊）.当0〈p〈1时l~p（X）非局部凸,但却是局部p-凸的,其共轭锥[l~p（X）]_p~＊充分大足以分离空间l~p（X）中点.本文探究0〈p〈1时l~p（X）的共轭锥[l~p（X）]_p~＊的表示问题,对于任意Banach空间X,得到次表示定理[l~p（X）]_p~＊■l~∞（X_p~＊）.对于数域X=R或C,次表示定理简化为[lp（R）]_p~＊■m~＋×m~＋与[l~p（C）]_p~＊■mM_p~＋（T）.

英文摘要：

For a Banach space X,it is well known that the dual of l~1（X） can be represented as l~∞（X~＊）.l~p（X） is not locally convex if 0p1,but it is locally p-convex,its conjugate cone[l~p（X）]_p~＊ is large enough to separate its points.This paper explores the representation problem of the conjugate cone of l~p（X）（0p1）,and obtains the Subrepresentation Theorem [l~o（X）]_p~＊■l~∞（X_p~＊） for every Banach space X.When X=R or C,the subrepresentation theorem has the simplified version[l~p（R）]_p~＊■m＋×m~＋and[l~p（C）]_p~＊■mM_p~＋（T） respectively.