Let $X$ be a Banach space and $I \in L(X)$ be the identity operator. Determine the action of the operator $e^I$ on $X$.
Pretty stuck here, not sure exactly what it means by determine the action. Very little ideas with this question really
2026-04-01 17:27:18.1775064438
The exponential of the identity operator in a Banach space
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A thought to get started: write a power series for $e^I$. See anything simple to do? If you don't like the idea of just jumping to a full series, start with a partial sum and see what comes out.