On closed subspaces with Schauder bases in non-archimedean Frechet spaces
| dc.contributor.author | Śliwa, Wiesław | |
| dc.date.accessioned | 2011-02-28T07:23:13Z | |
| dc.date.available | 2011-02-28T07:23:13Z | |
| dc.date.issued | 2001-12 | |
| dc.description.abstract | The main purpose of this paper is to prove that a non-archimedean Frechet space of countable type is normable (respectively nuclear; reflexive; a Monte1 space) if and only if any its closed subspace with a Schauder basis is normable (respectively nuclear; reflexive; a Monte1 space). It is also shown that any Schauder basis in a non-normable non-archimedean Frechet space has a block basic sequence whose closed linear span is nuclear. It follows that any non-normable non-archimedean Frechet space contains an infinite-dimensional nuclear closed subspace with a Schauder basis. Moreover, it is proved that a non-archimedean Frechet space E with a Schauder basis contains an infinite-dimensional complemented nuclear closed subspace with a Schauder basis if and only if any Schauder basis in E has a subsequence whose closed linear span is nuclear. | pl_PL |
| dc.identifier.citation | Indag. Mathem., (N.S.), 12(4),519-531. | pl_PL |
| dc.identifier.uri | http://hdl.handle.net/10593/916 | |
| dc.language.iso | en | pl_PL |
| dc.publisher | Royal Netherlands Academy of Arts and Sciences | pl_PL |
| dc.title | On closed subspaces with Schauder bases in non-archimedean Frechet spaces | pl_PL |
| dc.type | Article | pl_PL |