On automorphisms of L.C. groups
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- by Justin Peters PDF
- Proc. Amer. Math. Soc. 65 (1977), 347-350 Request permission
Abstract:
The left regular representation $\lambda$ of a locally compact group G generates a ${W^\ast }$-algebra $\mathcal {R}(\lambda )$, and each topological automorphism $\tilde \alpha$ of G has a natural extension to an automorphism $\tilde \alpha$ of $\mathcal {R}(\lambda )$. It is proved that an automorphism $\beta$ of $\mathcal {R}(\lambda )$ is of the form $\beta = \tilde \alpha$ for $\alpha \in {\operatorname {Aut}}(G)$ iff $\beta$ leaves a certain cone in $\mathcal {R}(\lambda )$ invariant.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 347-350
- MSC: Primary 22D45
- DOI: https://doi.org/10.1090/S0002-9939-1977-0450457-2
- MathSciNet review: 0450457