# Nuclear Space problem

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

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Dear Koushik, What do you mean by $C(X)$? Regards, –  Emerton Jan 4 '13 at 13:53
The only nuclear Banach spaces are the finite-dimensional ones. So I repeat the question: what is $C(X)$? en.wikipedia.org/wiki/Nuclear_space –  Gerald Edgar Jan 4 '13 at 14:36
He is talking about en.wikipedia.org/wiki/Nuclear_C*-algebra –  Tomek Kania Jan 4 '13 at 14:45
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 Margetts Jan 5 '13 at 4:48
I have talked with Ollie and solved it. –  Koushik Jan 6 '13 at 2:51