Unitary $\textbf {Z}^ d$-actions with continuous spectrum
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- by Vitaly Bergelson, Isaac Kornfeld and Boris Mityagin PDF
- Proc. Amer. Math. Soc. 119 (1993), 1127-1134 Request permission
Abstract:
For any unitary ${\mathbb {Z}^d}$-action on a Hilbert space with continuous spectrum weakly wandering vectors are dense. This wandering can be forced to occur along $IP$-sets. This is a generalization and strengthening of a result due to Krengel. Our method is based on the contractive mapping fixed-point theorem.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 1127-1134
- MSC: Primary 47A35; Secondary 47B99
- DOI: https://doi.org/10.1090/S0002-9939-1993-1145413-4
- MathSciNet review: 1145413