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Results tagged with locally-convex-spaces
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user 2622
Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.
5
votes
2
answers
541
views
Existence of a countable linear combination with positive coefficients
Consider a (Hausdorff and complete) locally convex topological vector space $V$ and a countable subset $(v_k)_{k=1}^\infty \subset V$ of non-zero vectors.
$(*)$ Under what conditions on this subse …
4
votes
1
answer
794
views
Hahn-Banach restricted to a pre-dual
If $V$ is a locally convex topological space, the Hahn-Banach theorem shows that a continuous linear functional on a closed subspace can be extended to a continuous linear functional on all of $V$, th …
- 7,426