Topological properties and matrix transformations of certain ordered generalized sequence spaces
In this note, we carry out investigations related to the mixed impact of ordering and topological structure of a locally convex solid Riesz space (X,τ) and a scalar valued sequence space λ, on the vector valued sequence space λ(X) which is formed and topologized with the help of λ and X, and vice ve...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000433 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558721669005312 |
|---|---|
| author | Manjul Gupta Kalika Kaushal |
| author_facet | Manjul Gupta Kalika Kaushal |
| author_sort | Manjul Gupta |
| collection | DOAJ |
| description | In this note, we carry out investigations related to the mixed
impact of ordering and topological structure of a locally convex solid
Riesz space (X,τ) and a scalar valued sequence space λ, on the vector
valued sequence space λ(X) which is formed and topologized with the help
of λ and X, and vice versa. Besides,we also characterize o-matrix transformations
from c(X), ℓ∞(X) to themselves, cs(X) to c(X) and derive necessary
conditions for a matrix of linear operators to transform ℓ1(X) into a
simple ordered vector valued sequence space Λ(X). |
| format | Article |
| id | doaj-art-4e6e3372ef36441988ed1fae4fdced22 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4e6e3372ef36441988ed1fae4fdced222025-02-03T01:31:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118234135610.1155/S0161171295000433Topological properties and matrix transformations of certain ordered generalized sequence spacesManjul Gupta0Kalika Kaushal1Department of Mathematics, Indian Institute of Technology, Kanpur 208016, IndiaDepartment of Mathematics, Indian Institute of Technology, Kanpur 208016, IndiaIn this note, we carry out investigations related to the mixed impact of ordering and topological structure of a locally convex solid Riesz space (X,τ) and a scalar valued sequence space λ, on the vector valued sequence space λ(X) which is formed and topologized with the help of λ and X, and vice versa. Besides,we also characterize o-matrix transformations from c(X), ℓ∞(X) to themselves, cs(X) to c(X) and derive necessary conditions for a matrix of linear operators to transform ℓ1(X) into a simple ordered vector valued sequence space Λ(X).http://dx.doi.org/10.1155/S0161171295000433Riesz spacesorder completeidealdiagonal property; positivesequentially order continuous and o-precompact linear operators; locally convex solid Riesz spacesRiesz seminormsLebesgue pre-LebesgueFatau property; ordered vector valued sequence spaces matrix transformations. |
| spellingShingle | Manjul Gupta Kalika Kaushal Topological properties and matrix transformations of certain ordered generalized sequence spaces International Journal of Mathematics and Mathematical Sciences Riesz spaces order complete ideal diagonal property; positive sequentially order continuous and o-precompact linear operators; locally convex solid Riesz spaces Riesz seminorms Lebesgue pre-Lebesgue Fatau property; ordered vector valued sequence spaces matrix transformations. |
| title | Topological properties and matrix transformations of certain ordered generalized sequence spaces |
| title_full | Topological properties and matrix transformations of certain ordered generalized sequence spaces |
| title_fullStr | Topological properties and matrix transformations of certain ordered generalized sequence spaces |
| title_full_unstemmed | Topological properties and matrix transformations of certain ordered generalized sequence spaces |
| title_short | Topological properties and matrix transformations of certain ordered generalized sequence spaces |
| title_sort | topological properties and matrix transformations of certain ordered generalized sequence spaces |
| topic | Riesz spaces order complete ideal diagonal property; positive sequentially order continuous and o-precompact linear operators; locally convex solid Riesz spaces Riesz seminorms Lebesgue pre-Lebesgue Fatau property; ordered vector valued sequence spaces matrix transformations. |
| url | http://dx.doi.org/10.1155/S0161171295000433 |
| work_keys_str_mv | AT manjulgupta topologicalpropertiesandmatrixtransformationsofcertainorderedgeneralizedsequencespaces AT kalikakaushal topologicalpropertiesandmatrixtransformationsofcertainorderedgeneralizedsequencespaces |