Let-E-be-a-banach-space-Y-is-normed-space-and-suppose-that-Ta-a-A-B-E-Y-If-Tax-a-A-Y-is-bounded-for-all-x-E-then-Ta-a-A-is-bounded-

Question Number 7499 by Tawakalitu. last updated on 31/Aug/16

L e t E b e a b a n a c h s p a c e, Y i s n o r m e d s p a c e a n d

s u p p o s e t h a t {T a : a \in A} \subseteq B (E, Y) I f {T a x : a \in A}

\subseteq Y i s b o u n d e d, f o r a l l x \in E, t h e n {∥ T a ∥ : a \in A} i s

b o u n d e d .