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Proceedings of the American Mathematical Society

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

 
 

 

Unitary $ {\bf Z}\sp d$-actions with continuous spectrum


Authors: Vitaly Bergelson, Isaac Kornfeld and Boris Mityagin
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
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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 [Enhancements On Off] (What's this?)

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  • [K] U. Krengel, Weakly wandering vectors and weakly independent partitions, Trans. Amer. Math. Soc. 164 (1972), 199-226. MR 0290168 (44:7353)
  • [KN] B. Koopman and J. von Neumann, Dynamical systems of continuous spectra, Proc. Nat. Acad. Sci. U.S.A. 18 (1931), 255-263.

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DOI: https://doi.org/10.1090/S0002-9939-1993-1145413-4
Article copyright: © Copyright 1993 American Mathematical Society

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