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Results tagged with topological-vector-spaces
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user 109133
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.
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Complete dual of bornological space
A bornologigal topological vector space is such that any bounded linear function on it is continuous. It is a standard result [Jarchow, Locally convex spaces, 1981] that if the dual $E'$ of a Mackey s …
- 103
4
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DF-spaces and F spaces
It is well known that when $E$ is a $DF$-space and $F$ is a Fréchet space, the space $\mathcal{L}_{b} (E,F)$ is Fréchet. The converse, that is the fact that $\mathcal{L}_{b} (F,E)$ would be $DF$, is i …
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