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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203302315 |
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| _version_ | 1832552692571963392 |
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| author | Elizabeth M. Bator Dawn R. Slavens |
| author_facet | Elizabeth M. Bator Dawn R. Slavens |
| author_sort | Elizabeth M. Bator |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-216ee22562d34931bcbc9906ccbc45f0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-216ee22562d34931bcbc9906ccbc45f02025-02-03T05:57:57ZengWileyInternational 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 |
| spellingShingle | Elizabeth M. Bator Dawn R. Slavens DP1 and completely continuous operators International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | DP1 and completely continuous operators |
| title_sort | dp1 and completely continuous operators |
| url | http://dx.doi.org/10.1155/S0161171203302315 |
| work_keys_str_mv | AT elizabethmbator dp1andcompletelycontinuousoperators AT dawnrslavens dp1andcompletelycontinuousoperators |