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Question about Functional Analysis (uniform boundedness)

https://workspace.imperial.ac.uk/people/Public/O.Pocovnicu/Coursework_week_5.pdf
Question 1.

So I proved it using uniform boundedness. But why can we not just say B(xn,yn) = B(xn,0) + B(0,yn) and then let n go to infinity for a 1 line proof?

EDIT: Delete this. I figured it out!
(edited 11 years ago)

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