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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000160 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |