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<∞, (⊕α∈𝒜Xα)p has the DP1 property if and only if each Xα does. This is not the case for (⊕α∈𝒜Xα)∞. In fact, we show that (⊕α∈𝒜Xα)∞ has the DP1 property if and only if it ha...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2003-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203302315 |
| id |
doaj-216ee22562d34931bcbc9906ccbc45f0 |
|---|---|
| record_format |
Article |
| spelling |
doaj-216ee22562d34931bcbc9906ccbc45f02020-11-25T00:02:03ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003372375237810.1155/S0161171203302315DP1 and completely continuous operatorsElizabeth M. Bator0Dawn R. Slavens1Department of Mathematics, University of North Texas, P.O. Box 311400, Denton 76203-1400, TX, USADepartment of Mathematics, Midwestern State University, 3410 Taft Blvd, Wichita Falls 76308, TX, USAW. Freedman introduced an alternate to the Dunford-Pettis property, called the DP1 property, in 1997. He showed that for 1≤p<∞, (⊕α∈𝒜Xα)p has the DP1 property if and only if each Xα does. This is not the case for (⊕α∈𝒜Xα)∞. In fact, we show that (⊕α∈𝒜Xα)∞ 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.http://dx.doi.org/10.1155/S0161171203302315 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Elizabeth M. Bator Dawn R. Slavens |
| spellingShingle |
Elizabeth M. Bator Dawn R. Slavens DP1 and completely continuous operators International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Elizabeth M. Bator Dawn R. Slavens |
| author_sort |
Elizabeth M. Bator |
| title |
DP1 and completely continuous operators |
| title_short |
DP1 and completely continuous operators |
| title_full |
DP1 and completely continuous operators |
| title_fullStr |
DP1 and completely continuous operators |
| title_full_unstemmed |
DP1 and completely continuous operators |
| title_sort |
dp1 and completely continuous operators |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2003-01-01 |
| description |
W. Freedman introduced an alternate to the
Dunford-Pettis property, called the DP1 property,
in 1997. He showed that for 1≤p<∞,
(⊕α∈𝒜Xα)p has the DP1 property if and only if each Xα does. This is not the case for (⊕α∈𝒜Xα)∞. In
fact, we show that (⊕α∈𝒜Xα)∞ 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. |
| url |
http://dx.doi.org/10.1155/S0161171203302315 |
| work_keys_str_mv |
AT elizabethmbator dp1andcompletelycontinuousoperators AT dawnrslavens dp1andcompletelycontinuousoperators |
| _version_ |
1725439678167908352 |