- #1
Jaggis
- 36
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Hi, I have some trouble with the following problem:
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?
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?