Spectral properties of dynamical tensor powers, and tensor factorizations of simple Lebesgue spectrum
Abstract
For every $n>0$ there is a unitary operator $U$ such that the unitary operator with simple Lebesgue spectrum is isomorphic to the tensor product $U\otimes U^2\otimes\dots\otimes U^{2^n}.$ There is an ergodic automorphism $T$ with its symmetric tensor power $T^{\odot n}$ of simple spectrum, and $T^{\odot(n+1)}$ of absolutely continuous spectrum.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.08409
- arXiv:
- arXiv:2406.08409
- Bibcode:
- 2024arXiv240608409R
- Keywords:
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- Mathematics - Dynamical Systems