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ArticleOriginal scientific text

Title

Cyclic space isomorphism of unitary operators

Authors 1

Affiliations

  1. Department of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

We introduce a new equivalence relation between unitary operators on separable Hilbert spaces and discuss a possibility to have in each equivalence class a measure-preserving transformation.

Bibliography

  1. O. N. Ageev, Dynamical systems with a Lebesgue component of even multiplicity in the spectrum, Mat. Sb. 136 (178) (1988), 307-319 (in Russian); English transl.: Math. USSR-Sb. 64 (1989), 305-317.
  2. F. Blanchard and M. Lemańczyk, Measure preserving diffeomorphisms with an arbitrary spectral multiplicity, Topol. Methods Nonlinear Anal. 1 (1993), 275-294.
  3. N. Dunford and T. Schwartz, Linear Operators, Wiley-Interscience, 1971.
  4. G. R. Goodson, J. Kwiatkowski, M. Lemańczyk and P. Liardet, On the multiplicity function of ergodic group extensions of rotations, Studia Math. 102 (1992), 157-174.
  5. J. Kwiatkowski Jr. and M. Lemańczyk, On the multiplicity function of ergodic group extensions. II, Studia Math. 116 (1995), 207-215.
  6. M. Lemańczyk, Toeplitz Z2-extensions, Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), 1-43.
  7. J. Mathew and M. G. Nadkarni, A measure preserving transformation whose spectrum has Lebesgue component of multiplicity two, Bull. London Math. Soc. 16 (1984), 402-406.
  8. M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, Lecture Notes in Math. 1294, Springer, Berlin, 1987.
  9. W. Parry, Topics in Ergodic Theory, Cambridge Univ. Press., Cambridge, 1981.
  10. E. A. Robinson, Ergodic measure preserving transformations with arbitrary finite spectral multiplicities, Invent. Math. 72 (1983), 299-314.
  11. E. A. Robinson, Transformations with highly nonhomogeneous spectrum of finite multiplicity, Israel J. Math. 56 (1986), 75-88.
Studia Mathematica
1997/124/3
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Pages:
259-267
Main language of publication
English
Received
1996-02-26
Accepted
1997-01-20
Published
1997
Exact and natural sciences