【摘要】 二重序列空间是一类重要的Banach序列空间,而这类空间的连续线性泛函的表示还没有完全清楚。l←pq是一类二重序列空间,就该空间在范围0<p,q≤1内讨论其连续线性泛函的表示。首先证明了{eij}∞i,j=1是空间l←pq的一组Schauder基,并在此基础上研究了二重序列空间l←pq的连续线性泛函的表示,证明了空间l←pq的对偶空间为(l←pq) =l←∞∞。更多还原

【Abstract】 Double sequence space is a kind of important Banach sequence space, but the expression of this kind of spaces’ continuous linear functional is not completely clear. l_←（pq） is a sort of double sequence space, in which the expression of continuous linear functional was talked about when 0<p,q≤1.Firstly, {e_ij}^∞_i,j=1 being Schander basis of space l_←（pq）was proved. Based on the result, the expression of continuous linear functional of the space l_←（pq） was also studied. The dual space of double sequence space l_←（pq） being (l_←（pq）)^*=l_{←（∞∞）} was proved.更多还原