I have a problem. Somehow it doesn't seem all that tricky but I just can't get my head around it. Ok, here it goes: Let be Banach spaces and let be a map satisfying: for fixed in is linear and continuous (and the same for a fixed in ). How do I show that my map is continuous aswell.
First I was thinking that I should just simply show that it is bdd using the continuity in the two cases but I can't really manage.