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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171296000907 |
| Summary: | 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). |
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| ISSN: | 0161-1712 1687-0425 |