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On the Commutant of Certain Automorphism Groups

Published online by Cambridge University Press:  20 November 2018

P. K. Tam
P. K. Tam*
Affiliation:
The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
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Let be a W*-algebra, A ( ) the group of all automorphisms of . In this paper we have determined the commutant G’ of a subgroup G of A () for certain classes of G and . The main results are as follows.

Theorem 1. If G is a locally compact abelian group acting by translation on the W*-algebra L∞(G), then the commutant of a dense subgroup of G is G itself.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1165 - 1169
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bures, D., Certain factors constructed as infinite tensor products, Compositio Math. 15 (1963), 169–191.Google Scholar
2. Bures, D., Abelian subalgebras of von Neumann algebras (to appear in Mem. Amer. Math. Soc).Google Scholar
3. Bures, D., An extension of Kautani's theorem on infinite product measures to the tensor product of semi-finite W*-algebras, Trans. Amer. Math. Soc. 135 (1969), 199–212.Google Scholar
4. Kakutani, S., On equivalence of infinite product measures, Ann. of Math. 49 (1948), 214–226.Google Scholar
5. Neumann, J. von, On infinite direct products, Compositio Math. 6 (1938), 1–77.Google Scholar
6. Pukánszky, L., Some examples of factors, Publ. Math. Debrecen 4 (1956), 135–156.Google Scholar
7. Tarn, P. K., On unitary equivalence of certain classes of non-normal operators, Can. J. Math. 23 (1971), 849–856.Google Scholar