Asymptotically equicontinuous sequences of operators and a Banach-Steinhaus type theorem
| Autor: | Mashreghi, Javad, Ransford, Thomas |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We introduce the notion of an asymptotically equicontinuous sequence of linear operators, and use it to prove the following result. If $X,Y$ are topological vector spaces, if $T_n,T:X\to Y$ are continuous linear maps, and if $D$ is a dense subset of $X$, then the following statements are equivalent: (i) $T_nx\to Tx$ for all $x\in X$, and (ii) $T_n x\to Tx$ for all $x\in D$ and the sequence $(T_n)$ is asymptotically equicontinuous. |
| Databáze: | arXiv |
| Externí odkaz: |
|