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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 at 13:53
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 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 at 14:36
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 He is talking about en.wikipedia.org/wiki/Nuclear_C*-algebra – Tomek Kania Jan 4 at 14:45
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 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 at 4:48
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 I have talked with Ollie and solved it. – Koushik Jan 6 at 2:51
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