@article { author = {Mashreghi, J. and Ransford, T.}, title = {Asymptotically equicontinuous sequences of operators and a Banach--Steinhaus type theorem}, journal = {Journal of the Iranian Mathematical Society}, volume = {3}, number = {2}, pages = {43-47}, year = {2022}, publisher = {Iranian Mathematical Society}, issn = {2717-1612}, eissn = {2717-1612}, doi = {10.30504/jims.2022.361848.1073}, abstract = {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.}, keywords = {Banach-Steinhaus theorem,dense,equicontinuous}, url = {https://jims.ims.ir/article_158793.html}, eprint = {https://jims.ims.ir/article_158793_4504b652d02694be4d859572ff4f36e6.pdf} }