Stone’s theorem and spectral subspaces of automorphisms

Størmer, Erling

doi:10.1090/S0002-9939-1978-0467342-3

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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Stone’s theorem and spectral subspaces of automorphisms
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Proc. Amer. Math. Soc. 70 (1978), 18-20 Request permission

Abstract:

It is shown that spectral subspaces of automorphisms of a von Neumann algebra can be defined by use of Stone’s theorem on unitary representations.

References

William Arveson, On groups of automorphisms of operator algebras, J. Functional Analysis 15 (1974), 217–243. MR 0348518, DOI 10.1016/0022-1236(74)90034-2
H. J. Borchers, Über Ableitungen von $C^{\ast }$-Algebren, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1973), 19–35 (German). MR 353001
Alain Connes, Une classification des facteurs de type $\textrm {III}$, Ann. Sci. École Norm. Sup. (4) 6 (1973), 133–252 (French). MR 341115, DOI 10.24033/asens.1247