Is a Limited Operator Equivalent to Continuity in Norm Topology?

[diegzumillo]

Hi there! :)

I'm trying to understand a theorem, but it's full with analysis (or something) terms unfamiliar to me.

Is there an intuitive interpretation for the sentence: 'An operator being limited is equivalent to continuity in the topolgy of the norm'?

Also, how can I partially understand what is a "strongly continuous application"?

I understand that for a plain comprehension, one is required to follow a strict study on these subjects. But right now I'm happy with a simple intuition.

Edit: Is this the right place? I'm not sure analysis is the subject here!

 

[Fredrik]

Check out the Wikipedia entry on "bounded operator". It contains an easy proof.

I agree that it's hard to figure out where to put a post about functional analysis. Strangerep and I were just saying that in another thread.

 

[diegzumillo]

Thanks Fredrik!

(I thought I subscribed to thread!)