不存在非零连续线性算子的拓扑向量空间对

如果拓扑向量空间（ＴＶＳ）Ｘ中的任意拟有界集均为有界集，则称Ｘ有ＰＢ－Ｂ性质，证明了：（ａ）局部拟凸的ＴＶＳ具有ＰＢ－Ｂ性质；（ｂ）局部有界当且仅当局部拟有界且局部拟凸；（ｃ）不存在从拟有界ＴＶＳ到具有ＰＢ－Ｂ性质且满意Ｔ０公理的ＴＶＳ的非零连续线性算子。

The TVS Pairs of Non existence of Non zero Continuous Linear Operators

Say that a topological vector space (TVS) admits PB B property if every pseudobounded subset of it is bounded.Proves that (a)every locally pseudoconvex TVS admifs PB B property,(b)X is locally bounded if and only if it is locally pseudobounded and locally pseudoconvex,(c)there is not any non zero continuous linear operator mapping a pseudobounded TVS into a TVS with T 0 and PB B property.