Cyclic space isomorphism of unitary operators

Krzysztof Frączek

Studia Mathematica (1997)

  • Volume: 124, Issue: 3, page 259-267
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Frączek, Krzysztof. "Cyclic space isomorphism of unitary operators." Studia Mathematica 124.3 (1997): 259-267. <http://eudml.org/doc/216413>.

@article{Frączek1997,
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.},
author = {Frączek, Krzysztof},
journal = {Studia Mathematica},
keywords = {cyclic subspace; cyclic space isomorphism; unitary operators; invertible measure preserving transformations},
language = {eng},
number = {3},
pages = {259-267},
title = {Cyclic space isomorphism of unitary operators},
url = {http://eudml.org/doc/216413},
volume = {124},
year = {1997},
}

TY - JOUR
AU - Frączek, Krzysztof
TI - Cyclic space isomorphism of unitary operators
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 3
SP - 259
EP - 267
AB - 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.
LA - eng
KW - cyclic subspace; cyclic space isomorphism; unitary operators; invertible measure preserving transformations
UR - http://eudml.org/doc/216413
ER -

References

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  1. [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. [2] F. Blanchard and M. Lemańczyk, Measure preserving diffeomorphisms with an arbitrary spectral multiplicity, Topol. Methods Nonlinear Anal. 1 (1993), 275-294. Zbl0793.28012
  3. [3] N. Dunford and T. Schwartz, Linear Operators, Wiley-Interscience, 1971. 
  4. [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. Zbl0830.28009
  5. [5] J. Kwiatkowski Jr. and M. Lemańczyk, On the multiplicity function of ergodic group extensions. II, Studia Math. 116 (1995), 207-215. Zbl0857.28012
  6. [6] M. Lemańczyk, Toeplitz Z 2 -extensions, Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), 1-43. 
  7. [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. Zbl0515.28010
  8. [8] M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, Lecture Notes in Math. 1294, Springer, Berlin, 1987. 
  9. [9] W. Parry, Topics in Ergodic Theory, Cambridge Univ. Press., Cambridge, 1981. Zbl0449.28016
  10. [10] E. A. Robinson, Ergodic measure preserving transformations with arbitrary finite spectral multiplicities, Invent. Math. 72 (1983), 299-314. Zbl0519.28008
  11. [11] E. A. Robinson, Transformations with highly nonhomogeneous spectrum of finite multiplicity, Israel J. Math. 56 (1986), 75-88. Zbl0614.28012

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