Definition:Bounded Linear Transformation/Topological Vector Space
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Theorem
Let $\GF \in \set {\R, \C}$.
Let $X$ and $Y$ be topological vector spaces over $\GF$.
Let $T : X \to Y$ be a linear transformation.
We say that $T$ is a bounded linear transformation if and only if:
- for each von Neumann-bounded subset $E$ of $X$, $T \sqbrk E$ is von Neumann-bounded.
Sources
- 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.31$: Bounded linear transformations