[分析] Banach space

[Jer1983 (stanley)]

Let C[a,b] be the collection of real-valued continuous functions.

Suppose f,f_1,f_2... in C[a,b] and define the inner product

(f,g) = ∫_a^b f(x)*g(x) dx and associated norm ||f|| = (f,g)^(1/2)

要怎麼證明 (C[a,b], ||f||) 不是 Banach space ?


謝謝

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