空间l_■的对偶空间  

Dual Space of Space l_■

作　　者：付莹[1] 范传强[1] 王晶昕[1] 

机构地区：[1]辽宁师范大学数学学院

出　　处：《辽宁石油化工大学学报》2005年第2期89-91,共3页Journal of Liaoning Petrochemical University

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←∞∞。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.

关 键 词：h—Banach空间 SCHAUDER基 对偶空间 

分 类 号：O177.2[理学—数学]