Dual pairs of sequence spaces
The paper aims to develop for sequence spaces E a general concept for reconciling certain results, for example inclusion theorems, concerning generalizations of the Köthe-Toeplitz duals E×(×∈{α,β}) combined with dualities (E,G),G⊂E×, and the SAK-property (weak sectional convergence). Taking Eβ:={(yk...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201011772 |
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| _version_ | 1832552035242737664 |
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| author | Johann Boos Toivo Leiger |
| author_facet | Johann Boos Toivo Leiger |
| author_sort | Johann Boos |
| collection | DOAJ |
| description | The paper aims to develop for sequence spaces E a general concept for reconciling certain results, for example inclusion theorems, concerning generalizations of the Köthe-Toeplitz duals E×(×∈{α,β}) combined with dualities (E,G),G⊂E×, and the SAK-property (weak sectional convergence). Taking
Eβ:={(yk)∈ω:=𝕜ℕ|(ykxk)∈cs}=:Ecs, where cs denotes the set of all summable sequences, as a starting point, then we get a general substitute of Ecs by replacing cs by any locally convex sequence space S with sum s∈S′ (in particular, a sum space) as defined by Ruckle (1970). This idea provides a dual pair (E,ES) of sequence spaces and gives rise for a generalization of the
solid topology and for the investigation of the continuity of
quasi-matrix maps relative to topologies of the duality
(E,Eβ). That research is the basis for general versions of three types of inclusion theorems: two of them are originally due to Bennett and Kalton (1973) and generalized by the authors (see Boos and Leiger (1993 and 1997)), and the third was done by
Große-Erdmann (1992). Finally, the generalizations, carried out in this paper, are justified by four applications with results around different kinds of Köthe-Toeplitz duals and
related section properties. |
| format | Article |
| id | doaj-art-a9f4c2e96328431eb3424928f84bb36a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a9f4c2e96328431eb3424928f84bb36a2025-02-03T05:59:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0128192310.1155/S0161171201011772Dual pairs of sequence spacesJohann Boos0Toivo Leiger1Fachbereich Mathematik, Fern Universität Hagen, Hagen D-58084, GermanyPuhta Matemaatika Instituut, Tartu Ülikool, Tartu EE 50090, EstoniaThe paper aims to develop for sequence spaces E a general concept for reconciling certain results, for example inclusion theorems, concerning generalizations of the Köthe-Toeplitz duals E×(×∈{α,β}) combined with dualities (E,G),G⊂E×, and the SAK-property (weak sectional convergence). Taking Eβ:={(yk)∈ω:=𝕜ℕ|(ykxk)∈cs}=:Ecs, where cs denotes the set of all summable sequences, as a starting point, then we get a general substitute of Ecs by replacing cs by any locally convex sequence space S with sum s∈S′ (in particular, a sum space) as defined by Ruckle (1970). This idea provides a dual pair (E,ES) of sequence spaces and gives rise for a generalization of the solid topology and for the investigation of the continuity of quasi-matrix maps relative to topologies of the duality (E,Eβ). That research is the basis for general versions of three types of inclusion theorems: two of them are originally due to Bennett and Kalton (1973) and generalized by the authors (see Boos and Leiger (1993 and 1997)), and the third was done by Große-Erdmann (1992). Finally, the generalizations, carried out in this paper, are justified by four applications with results around different kinds of Köthe-Toeplitz duals and related section properties.http://dx.doi.org/10.1155/S0161171201011772 |
| spellingShingle | Johann Boos Toivo Leiger Dual pairs of sequence spaces International Journal of Mathematics and Mathematical Sciences |
| title | Dual pairs of sequence spaces |
| title_full | Dual pairs of sequence spaces |
| title_fullStr | Dual pairs of sequence spaces |
| title_full_unstemmed | Dual pairs of sequence spaces |
| title_short | Dual pairs of sequence spaces |
| title_sort | dual pairs of sequence spaces |
| url | http://dx.doi.org/10.1155/S0161171201011772 |
| work_keys_str_mv | AT johannboos dualpairsofsequencespaces AT toivoleiger dualpairsofsequencespaces |