The group of automorphisms of 𝐿¹(0,1) is connected

Ghahramani, F.

doi:10.1090/S0002-9947-1989-0937244-6

The group of automorphisms of $L^ 1(0,1)$ is connected
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Trans. Amer. Math. Soc. 314 (1989), 851-859 Request permission

Abstract:

It is shown that the group of the automorphisms of the radical convolution algebra ${L^1}(0,1)$ is connected in the operator norm topology, and thus every automorphism is of the form ${e^{\lambda d}}{e^q}$, where $\lambda$ is a complex number, $d$ is the derivation $df(x) = xf(x)$ and $q$ is a quasinilpotent derivation.

References

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