- #1
Calabi
- 140
- 2
Homework Statement
Let be E a normded vectoriel space, ##dim(E) = m \in \mathbb{N}^{*}##, I have to show that ##\exists \rho_{1}, \rho_{2} > 0 | \forall u \in L(E), ||u^{m} - Id| \leq \rho_{1} \Rightarrow |u - Id| \leq \rho_{2}##.
Homework Equations
Nothing.
The Attempt at a Solution
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I try to constrcut a ##C^{1}## application which will have by definition a continuous différential. But I don't see what the dimension m as to do in here and I'm really locked.
Could you give me a clue please?
Thank you in advance and have a nice afternoon.