Gliding hump properties and some applications
In this not we consider several types of gliding bump properties for a sequence space E and we consider the various implications between these properties. By means of examples we show that most of the implications are strict and they afford a sort of structure between solid sequence spaces and those...
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| Format: | Article |
| Language: | English |
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Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171295000160 |
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| _version_ | 1841524539574452224 |
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| author | Johann Boos Daniel J. Fleming |
| author_facet | Johann Boos Daniel J. Fleming |
| author_sort | Johann Boos |
| collection | DOAJ |
| description | In this not we consider several types of gliding bump properties for a sequence space E
and we consider the various implications between these properties. By means of examples we show that
most of the implications are strict and they afford a sort of structure between solid sequence spaces and
those with weakly sequentially complete β-duals. Our main result is used to extend a result of Bennett and
Kalton which characterizes the class of sequence spaces E with the properly that E⊂SF, whenever F is
a separable FK space containing E where SF denotes the sequences in F having sectional convergence.
This, in turn, is used to identify a gliding humps property as a sufficient condition for E to be in this
class. |
| format | Article |
| id | doaj-art-5354ebdfab91454599c886ac17002a4e |
| 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-5354ebdfab91454599c886ac17002a4e2025-02-03T05:52:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118112113210.1155/S0161171295000160Gliding hump properties and some applicationsJohann Boos0Daniel J. Fleming1Fachbereich Mathematik, FernUniversität Gesamthochschule, Hagen D 58084, GermanyDepartment of Mathematics, St. Lawrence Univesity, Canton 13617, NY, USAIn this not we consider several types of gliding bump properties for a sequence space E and we consider the various implications between these properties. By means of examples we show that most of the implications are strict and they afford a sort of structure between solid sequence spaces and those with weakly sequentially complete β-duals. Our main result is used to extend a result of Bennett and Kalton which characterizes the class of sequence spaces E with the properly that E⊂SF, whenever F is a separable FK space containing E where SF denotes the sequences in F having sectional convergence. This, in turn, is used to identify a gliding humps property as a sufficient condition for E to be in this class.http://dx.doi.org/10.1155/S0161171295000160gliding hump propertiesweak sequential completeness of the β-dual sectional convergence in FK spacestheorem of Schurtheorem of Hahu. |
| spellingShingle | Johann Boos Daniel J. Fleming Gliding hump properties and some applications International Journal of Mathematics and Mathematical Sciences gliding hump properties weak sequential completeness of the β-dual sectional convergence in FK spaces theorem of Schur theorem of Hahu. |
| title | Gliding hump properties and some applications |
| title_full | Gliding hump properties and some applications |
| title_fullStr | Gliding hump properties and some applications |
| title_full_unstemmed | Gliding hump properties and some applications |
| title_short | Gliding hump properties and some applications |
| title_sort | gliding hump properties and some applications |
| topic | gliding hump properties weak sequential completeness of the β-dual sectional convergence in FK spaces theorem of Schur theorem of Hahu. |
| url | http://dx.doi.org/10.1155/S0161171295000160 |
| work_keys_str_mv | AT johannboos glidinghumppropertiesandsomeapplications AT danieljfleming glidinghumppropertiesandsomeapplications |