For any given distribution $T\in D'(\Omega)$, could $T$ has a coutinuous extension $$\widetilde{T}:C_0(\Omega)\rightarrow R,\ \ \ \widetilde{T}\in(C_0(\Omega))'\ \ ?$$ Could you state a general version of Hahn Banach Theorem, in which we don't require $T$ to be a continuous linear functional of a norm space?
2026-04-04 14:20:51.1775312451
Hahn Banach Theorem extending distribution
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