赋准范空间之间线性算子的五种有界性与连续性

The Five Boundedness and Continuity of Linear Operators between F*-Spaces

综合散见于多种文献的不同描述,明确线性算子拓扑有界、邻域有界、范有界与强有界的定义,引进次强有界的概念,给出赋准范空间之间与赋β-范空间之间线性算子的各种有界性以及连续性之间的关系定理与反例.

For linear operator, summing up the different descriptions scattered throughout a wide variety of literatures, this paper makes clear the definitions of topological boundedness, neighborhood boundedness, norm boundedness, strong boundedness, introduces the concept of sub-strong boundedness, and for linear operator between F＊-spaces and between β-normed spaces, gives the relationship theorems between various boundedness and continuity and some counter examples.