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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the spectral multiplicity of a class of finite rank transformations


Author: G. R. Goodson
Journal: Proc. Amer. Math. Soc. 93 (1985), 303-306
MSC: Primary 47A35; Secondary 28D05
MathSciNet review: 770541
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Abstract: The rank $ M$ transformations, which Chacon called the simple approximations with multiplicity $ M$, were shown by Chacon to have maximal spectral multiplicity at most $ M$, although no example was given where this bound is attained for $ M > 1$. In this paper, for each natural number $ M > 1$, we show how to construct a simple approximation with multiplicity $ M$ which is ergodic and has maximal spectral multiplicity equal to $ M - 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0770541-8
PII: S 0002-9939(1985)0770541-8
Article copyright: © Copyright 1985 American Mathematical Society