Definition:Balanced Set
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Definition
Let $\Bbb F \in \set {\R, \C}$.
Let $X$ be a vector space over $\Bbb F$.
Let $A \subseteq X$.
We say that $A$ is balanced if and only if:
- $s A \subseteq A$ for all $s \in \Bbb F$ with $\cmod s \le 1$
where $s A$ is the dilation of $A$ by $s$.
Also see
- Results about balanced sets can be found here.
Sources
- 2011: Graham R. Allan and H. Garth Dales: Introduction to Banach Spaces and Algebras ... (previous) ... (next): $2.1$: Normed Spaces