Definition:Von Neumann-Bounded Subset of Topological Vector Space
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Definition
Let $\Bbb F \in \set {\R, \C}$.
Let $\struct {X, \tau}$ be a topological vector space over $\Bbb F$.
Let $E \subseteq X$.
We say that $E$ is von Neumann-bounded if and only if:
- for each open neighbourhood $V$ of ${\mathbf 0}_X$, there exists $s > 0$ such that $E \subseteq t V$ for each $t > s$
where $t V$ is the dilation of $V$ by $t$.
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Also see
Source of Name
This entry was named for John von Neumann.
Sources
- 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.6$: Topological vector spaces