Abstract

We deal with barrelledness, distinguishedness and reflexivity properties in various weighted vector-valued summable sequence spaces, with weights in the $\alpha$-dual of a perfect scalar-valued sequence space $\Lambda$. A weaker notion of distinguishedness is introduced and characterized. A nice example showing the relevance of this notion is provided.

Keywords: Summable sequence space; barrelled space; distinguished space; reflexive space; AK-space.

MSC: 46A45, 46A03, 46A25, 46A08

DOI: 10.57016/MV-mm2H27K1

Pages:  1--11