I need to show that if X is compact,then C(X) is nuclear.Also is the condition X is metrisable
necessary. I am at present attending a conference "Recent Aadvances in Operator Theory". This
problem was given by Adam Skalski,Warshaw in the conference

Dear Koushik - seems odd to be communicating this way, since I'm also at the conference - but the proof can be gleaned using the CPA definition of nuclearity. Use the fact that C(X) has a partition of unity (look at Adam's notes to get an idea exactly how). If you want to find me I'm wearing a purple t-shirt with a man riding a dinosaur saying "To the disco!" :)
– Ollie MargettsJan 5 '13 at 4:48

2

I have talked with Ollie and solved it.
– KoushikJan 6 '13 at 2:51