Exercise 3, § 4

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

Spectral Theories, III, p. 123

Let $p\in [1,+\infty ]$ and $E =\ell^p_K(\mathbf{N})$ , and let $u$ be the shift endomorphism

(x_0, x_1, . . . ,)\mapsto (0, x_0, x_1, . . .)

of E. Now prove that $u$ is a Fredholm endomorphism of index 1 and that $((u)) = 1$ .

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