Non-archimedean Eberlein-mulian theory
It is shown that, for a large class of non-archimedean normed spaces E, a subset X is weakly compact as soon as f(X) is compact for all f∈E′ (Theorem 2.1), a fact that has no analogue in Functional Analysis over the real or complex numbers. As a Corollary we derive a non-archimedean version of the...
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Hindawi Limited
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000907 |
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doaj-4db61f2fdaf54fecac3d9fdb73f1272b2020-11-24T23:48:55ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119463764210.1155/S0161171296000907Non-archimedean Eberlein-mulian theoryT. Kiyosawa0W. H. Schikhof1Faculty of Education, Shizuoka University, Ohya, Shizuoka 422, JapanDepartment of Mathematics, University of Nijmegen, Toernooiveld, Nijmegen 6525 ED, The NetherlandsIt is shown that, for a large class of non-archimedean normed spaces E, a subset X is weakly compact as soon as f(X) is compact for all f∈E′ (Theorem 2.1), a fact that has no analogue in Functional Analysis over the real or complex numbers. As a Corollary we derive a non-archimedean version of the Eberlein-mulian Theorem (2.2 and 2.3, for the classical theorem, see [1], VIII, §2 Theorem and Corollary, page 219).http://dx.doi.org/10.1155/S0161171296000907Non-archimedean Banach spaceweak compactness. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
T. Kiyosawa W. H. Schikhof |
| spellingShingle |
T. Kiyosawa W. H. Schikhof Non-archimedean Eberlein-mulian theory International Journal of Mathematics and Mathematical Sciences Non-archimedean Banach space weak compactness. |
| author_facet |
T. Kiyosawa W. H. Schikhof |
| author_sort |
T. Kiyosawa |
| title |
Non-archimedean Eberlein-mulian theory |
| title_short |
Non-archimedean Eberlein-mulian theory |
| title_full |
Non-archimedean Eberlein-mulian theory |
| title_fullStr |
Non-archimedean Eberlein-mulian theory |
| title_full_unstemmed |
Non-archimedean Eberlein-mulian theory |
| title_sort |
non-archimedean eberlein-mulian theory |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1996-01-01 |
| description |
It is shown that, for a large class of non-archimedean normed spaces
E, a subset
X is weakly compact as soon as f(X) is compact for all f∈E′ (Theorem 2.1), a fact that has
no analogue in Functional Analysis over the real or complex numbers. As a Corollary we derive
a non-archimedean version of the Eberlein-mulian
Theorem (2.2 and 2.3, for the classical
theorem, see [1], VIII, §2 Theorem and Corollary, page 219). |
| topic |
Non-archimedean Banach space weak compactness. |
| url |
http://dx.doi.org/10.1155/S0161171296000907 |
| work_keys_str_mv |
AT tkiyosawa nonarchimedeaneberleinmuliantheory AT whschikhof nonarchimedeaneberleinmuliantheory |
| _version_ |
1725483979735302144 |