Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1985-0770541-8
MathSciNet review: 770541
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)

  • [1] J. R. Baxter, A class of ergodic transformations having simple spectrum, Proc. Amer. Math. Soc. 27 (1971), 275-279. MR 0276440 (43:2187)
  • [2] R. V. Chacon, Approximation and spectral multiplicity, Lecture Notes in Math., Vol. 160, Springer-Verlag, 1970, pp. 18-27. MR 0271303 (42:6186)
  • [3] A. Del Junco, A transformation wqith simple spectrum which is not rank one, Canad. J. Math. 29 (1977), 655-663. MR 0466489 (57:6367)
  • [4] N. A. Friedman, Introduction to ergodic theory, Van Nostrand, Princeton, N. J., 1970. MR 0435350 (55:8310)
  • [5] V. I. Oseledec, The spectrum of ergodic automorphisms, Dokl. Akad. Nauk SSSR 168 (1966), 776-779. (Russian) MR 0199347 (33:7494)
  • [6] W. Parry, Topics in ergodic theory, Cambridge Univ. Press, New York, 1981. MR 614142 (83a:28018)
  • [7] E. A. Robinson, Jr., Ergodic measure preserving transformations with arbitrary finite spectral multiplicities, Invent. Math. 72 (1983), 299-314. MR 700773 (85a:28014)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A35, 28D05

Retrieve articles in all journals with MSC: 47A35, 28D05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0770541-8
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society