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Results tagged with topological-vector-spaces
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user 49628
A topological vector space is a vector space $V$ over a topological field $\mathbb{K}$ (typically $\mathbb{K}=\mathbb{R}$ or $\mathbb{K}=\mathbb{C}$), together with a topology on $V$ such that vector addition and scalar multiplication are both continuous. Hilbert spaces and Banach spaces are examples of topological vector spaces.
6
votes
When sequentially continuous linear functional is continuous?
It is continuous even for the strong topology. This follows from general locally convex space theory, in particular from the fact that the space of smooth functions is a nuclear Fréchet space. Its d …
- 454
4
votes
Accepted
Linear operators on distributions with different topologies
The answer to all of your questions is no. This follows from the simple fact that if a linear mapping from a locally convex space $E$ into a normed space $F$ is continuous for the weak topology on $E …
- 454