The unique Jordan-Hahn decomposition property
✍ Scribed by Christian Schindler
- Publisher
- Springer US
- Year
- 1990
- Tongue
- English
- Weight
- 744 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0015-9018
No coin nor oath required. For personal study only.
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## Abstract We work in set theory ZF without axiom of choice. Though the Hahn‐Banach theorem cannot be proved in ZF, we prove that every Gateaux‐differentiable uniformly convex Banach space __E__ satisfies the following continuous Hahn‐Banach property: if __p__ is a continuous sublinear functional
The Jordan-Zassenhaus Theorem states that, if R is a Dedekind domain whose field Q of quotients is a global field, then for each R-order S in a semisimple algebra over Q, and for each positive integer n, there are only finitely many isomorphism classes of left S-lattices of rank ≤n. This result (whi