Geodesic
A Transformation with Simple Spectrum which is not Rank One
Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 655-663

Voir la notice de l'article provenant de la source Cambridge University Press

Following [10] an ergodic measure-preserving transformation is called rank one if it admits a sequence of approximating stacks. Rank one transformations have been studied in [1] and [2] where it was shown that any rank one transformation has simple spectrum. More generally it has been shown by Chacon [4] that a transformation of rank n has spectral multiplicity at most n. M. A. Akcoglu and J. R. Baxter have asked whether the converse is true. In particular: does simple spectrum imply rank one? In this paper we give a negative answer to this question. 
Junco, Andrés Del. A Transformation with Simple Spectrum which is not Rank One. Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 655-663. doi: 10.4153/CJM-1977-067-7
@article{10_4153_CJM_1977_067_7,
     author = {Junco, Andr\'es Del},
     title = {A {Transformation} with {Simple} {Spectrum} which is not {Rank} {One}},
     journal = {Canadian journal of mathematics},
     pages = {655--663},
     year = {1977},
     volume = {29},
     number = {3},
     doi = {10.4153/CJM-1977-067-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-067-7/}
}
TY  - JOUR
AU  - Junco, Andrés Del
TI  - A Transformation with Simple Spectrum which is not Rank One
JO  - Canadian journal of mathematics
PY  - 1977
SP  - 655
EP  - 663
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-067-7/
DO  - 10.4153/CJM-1977-067-7
ID  - 10_4153_CJM_1977_067_7
ER  - 
%0 Journal Article
%A Junco, Andrés Del
%T A Transformation with Simple Spectrum which is not Rank One
%J Canadian journal of mathematics
%D 1977
%P 655-663
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-067-7/
%R 10.4153/CJM-1977-067-7
%F 10_4153_CJM_1977_067_7

[1] 1. Baxter, J. R., A class of ergodic automorphisms, Thesis, University of Toronto, 1969. Google Scholar

[2] 2. Baxter, J. R. A class of ergodic transformations having simple spectrum, Proc. Amer. Math. Soc. 24 (1970). Google Scholar

[3] 3. Chacon, R. V., Weakly mixing transformations which are not strongly mixing, Proc. Amer. Math. Soc. 22 (1969), 559–562. Google Scholar

[4] 4. Chacon, R. V. Approximation and spectral multiplicity, Contributions to Ergodic Theory and Probability, Springer Lecture Notes 160 (1970), 18–27. Google Scholar

[5] 5. Friedman, N. A., Introduction to ergodic theory (Van Nostrand Reinhold, 1970). Google Scholar

[6] 6. Halmos, P. R., Ergodic theory (Chelsea, 1956). Google Scholar

[7] 7. del Junco, A., Transformations with discrete spectrum are stacking transformations, Can. J. Math. 28 (1976), 836–839. Google Scholar

[8] 8. Kakutani, S., On the ergodic theory of shift transformations, Proc. 5th Berkeley Symp. 2 part ii, 405–414. (University of Calif. Press, Berkeley, 1967). Google Scholar

[9] 9. Kakutani, S. Strictly ergodic symbolic dynamical systems, Proc. 6th Berkeley Symp. 2, 319–326 (University of Calif. Press, Berkeley, 1972). Google Scholar

[10] 10. Weiss, B., Equivalence of measure preserving transformations, preprint. Google Scholar

Cité par Sources :