Exercise 1, § 2

Tag 02RA, permanent. Cite it as [Bourbaki, Tag 02RA].

Spectral Theories, III, p. 118

Let $I = [a, b]$ be a compact interval of $\mathbf{R}$ . For every continuous function $f: I\rightarrow \mathbf{C}$ and every $y\in I$ , put

V(f)(y) =\int_a^yf(x)dx

Now prove that the linear mapping V from $\mathscr{C}(I)$ into $\mathscr{C}(I)$ is compact (« Volterra operator »).

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