Question

We have the following question of analysis :

Answer 1

Given \[\left\{ T_n \right\}\] is a sequence continuous linear map from normed space \[ (E,\left|| . \right||_E)\] into \[ (F,\left|| . \right||_F)\]. Suppose that \[\left\{ \left|| T_n \right|| \right\}\] is bounded and there exists a linear map T from E into F such that \[\left\{ T_n(x) \right\}\] converging to T(x) in F, \[\forall x \in E\]. Then I proved T is continuous on E.

But my question is : if \[\left\{ \left|| T_n \right|| \right\}\] is not bounded, then T is still continuous on E or not?

Answer 2

@rebeccaskell94 help

Answer 3

This is a bit advance for most of us in here, why don't you try math.stackexchange.com ?

Answer 4

I agree with @FoolForMath, but, after you do that you should come back and hang out, because we need more advanced math types around here :)

Answer 5

I just join the first foreign web, sorry all T_T

Answer 6

*bookmark