Hi, I have some trouble with the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

Let E be a Banach space.

Let A ∈ L(E), the space of linear operators from E.

Show that the linear operator φ: L(E) → L(E) with φ(T) = T + AT is an isomorphism if ||A|| < 1.

So the idea here is to use the Neumann series but I can't really figure out how to apply it here. Any help?

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# Neumann series

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