空间l→pq的对偶空间

辽宁石油化工大学学报 ›› 2005, Vol. 25 ›› Issue (2): 89-91.

空间l→_pq的对偶空间

付　莹^{1, 2} , 　范传强1 , 　王晶昕¹

1 .辽宁师范大学数学学院, 辽宁大连116029 ;
2 .抚顺职业技术学院, 辽宁抚顺113006

收稿日期:2005-03-05 出版日期:2005-06-20 发布日期:2017-04-18
作者简介:付莹(1971 -), 女, 辽宁抚顺市, 在读硕士。

Dual Space of Space l→_pq

1 .School of Mathematics , Liaoning Normal University , Dalian liaoning 116029 , P .R .China ;
2.Fushun Vocational Technology College , Fushun Liaoning 113006 , P .R .China

Received:2005-03-05 Published:2005-06-20 Online:2017-04-18

摘要/Abstract

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 → _∞∞。

关键词: 　h -Banach 空间, 　Schauder 基, 　对偶空间

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 w hen 0 < p , q ≤1 .Firstly , {eij}∞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

Key words: 　h -Banach space , 　Schauder basis, Dual space

付　莹, 范传强,王晶昕. 空间l→_pq的对偶空间[J]. 辽宁石油化工大学学报, 2005, 25(2): 89-91.

FU Ying,FAN Chuan -qiang,WANG Jing -xin. Dual Space of Space l→_pq[J]. Journal of Liaoning Petrochemical University, 2005, 25(2): 89-91.