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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The group of automorphisms of $ L\sp 1(0,1)$ is connected


Author: F. Ghahramani
Journal: Trans. Amer. Math. Soc. 314 (1989), 851-859
MSC: Primary 43A20; Secondary 43A22, 46J99
MathSciNet review: 937244
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0937244-6
Keywords: Automorphism, derivation, connectedness, quasinilpotent derivation
Article copyright: © Copyright 1989 American Mathematical Society