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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some weakly inner automorphisms of the Cuntz algebras
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by Sze-Kai Tsui PDF
Proc. Amer. Math. Soc. 123 (1995), 1719-1725 Request permission

Abstract:

Let V be an $n \times n$ unitary matrix. Then V induces an automorphism ${O_V}$ of ${O_\infty }$ and ${O_n}$. It is shown in this paper that ${O_V}$ is weakly inner. Let ${F_n}$ be the UHF ${C^ \ast }$-subalgebra of ${O_n}$ and U be a unitary operator in the diagonal maximal abelian $\ast$-subalgebra of ${F_n}$. Then the automorphism ${\lambda _U}$ of On defined by ${\lambda _U}({S_i}) = {U^ \ast }{S_i}$, for each generator ${S_i}$ of ${O_n}$, is weakly inner. Any automorphism conjugate to either one mentioned above is also weakly inner.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1719-1725
  • MSC: Primary 46L40; Secondary 46L05
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1239808-X
  • MathSciNet review: 1239808