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Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups

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Außenhofer L.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction...........................................................................................7 Notation...............................................................................................10 1. Auxiliary results in topology..............................................................11 2. Auxiliary results for topological groups............................................17 3. Elementary properties of homomorphism groups............................21 4. Homomorphism groups of abelian metrizable groups......................23 5. Some results in duality theory.........................................................25 6. Locally quasi-convex groups...........................................................30 7. Properties of the quasi-convex hull.................................................36 8. Reflexivity of locally convex vector spaces......................................40 9. Locally convex vector groups..........................................................46 10. Two representations of locally quasi-convex groups.....................48 11. The character groups of $L^p_ℤ([0,1])$ and $L^p([0,1])$............53 12. Free abelian topological groups...................................................58 13. C(K,𝕋) for compact K....................................................................63 14. The group C(X,𝕋)..........................................................................69 15. Duality theory for free abelian topological groups.........................71 16. A short survey of the theory of nuclear groups.............................73 17. Ellipsoids.......................................................................................73 18. Properties of the Kolmogorov diameter.........................................75 19. Gaussian-like measures................................................................86 20. Nuclear groups..............................................................................93 21. An embedding theorem for nuclear groups.................................104 22. The Bochner Theorem for nuclear groups..................................105 References........................................................................................111

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1 Außenhofer L.

1 1999

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Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups