数学季刊(英文版)
數學季刊(英文版)
수학계간(영문판)
CHINESE QUARTERLY JOURANL OF AMTHEMTICS
2001年
2期
30-36
,共7页
序列空间%σ-对偶%子级数收敛
序列空間%σ-對偶%子級數收斂
서렬공간%σ-대우%자급수수렴
本文研究了两类重要序列空间的σ-对偶.证明了局部凸空间的某些拓扑性质可用σ-对偶予以刻划.进一步地，一个Schur型结果和一个矩阵映象的自连续性结果被建立了.
本文研究瞭兩類重要序列空間的σ-對偶.證明瞭跼部凸空間的某些拓撲性質可用σ-對偶予以刻劃.進一步地，一箇Schur型結果和一箇矩陣映象的自連續性結果被建立瞭.
본문연구료량류중요서렬공간적σ-대우.증명료국부철공간적모사탁복성질가용σ-대우여이각화.진일보지，일개Schur형결과화일개구진영상적자련속성결과피건립료.
In this paper, the σ-duals of two classes important sequence spaces l1(X) and l∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ-duals. The criterions of bounded sets in l1(X) and l∞(X) with respect to the weak topologies generated by the σ-duals are obtained. Furthermore, a Schur type result and an automatic continuity theorem of matrix transformation are established.
