A note on nonlocally convex spaces whose large products (do not) contain \(\varphi_ d\). (English) Zbl 0745.46008
Summary: We give a theorem about the embedding of \(\varphi\), the countable- dimensional sum space, into large product spaces. This extends a result of Saxon to most nonlocally convex spaces. Then we show that there is no analogue of Saxon’s result for uncountable sum spaces.
MSC:
| 46A16 | Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) |
| 46A45 | Sequence spaces (including Köthe sequence spaces) |
| 46A03 | General theory of locally convex spaces |
