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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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exp(S) exp(T) = exp(S+T) for commuting operators

The standard way to prove the exponential law for two bounded commuting operators $S, T$ $$ \exp(S)\exp(T) = \exp(S+T) $$ is to pass by the binomial formula and the power series of $\exp(.)$. I wonder …
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