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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The group of automorphisms of $L^ 1(0,1)$ is connected
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by F. Ghahramani PDF
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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 314 (1989), 851-859
  • MSC: Primary 43A20; Secondary 43A22, 46J99
  • DOI: https://doi.org/10.1090/S0002-9947-1989-0937244-6
  • MathSciNet review: 937244