A note on the Banach-Steinhaus theorem
Let \((T_ i)\) be a family of bounded linear operators between Banach spaces such that \(\sup | T_ i|=\infty\). By the Banach-Steinhaus theorem, the set \(E=\{x:\) \(\sup | T_ i x|<\infty\}\) is `thin', namely a countable union of nowhere dense sets. Here it is shown that \(E\) is also thin in a different sense: it is a countable union of so-called porous sets.
family of bounded linear operators between Banach spaces
scientific article; zbMATH DE number 54518