DP1 AND COMPLETELY CONTINUOUS OPERATORS
W. Freedman introduced an alternate to the Dunford‐Pettis property, called the DP1 property, in 1997. He showed that for 1 ≤ p < ∞ , has the DP1 property if and only if each X α does. This is not the case for . In fact, we show that has the DP1 property if and only if it has the Dunford‐Pettis pr...
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| Vydáno v: | International Journal of Mathematics and Mathematical Sciences Ročník 2003; číslo 37; s. 2375 - 2378-180 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Hindawi Limiteds
2003
Wiley |
| ISSN: | 0161-1712, 1687-0425 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | W. Freedman introduced an alternate to the
Dunford‐Pettis property, called the DP1 property,
in 1997. He showed that for 1 ≤
p
<
∞
,
has the DP1 property if and only if each
X
α
does. This is not the case for . In
fact, we show that has the DP1 property if and only if it has
the Dunford‐Pettis property. A similar result also
holds for vector‐valued continuous function spaces. |
|---|---|
| Bibliografie: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0161-1712 1687-0425 |
| DOI: | 10.1155/S0161171203302315 |