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• # Artykuł - szczegóły

## Colloquium Mathematicum

2008 | 110 | 1 | 201-204

## Note on the isomorphism problem for weighted unitary operators associated with a nonsingular automorphism

EN

### Abstrakty

EN
We give a negative answer to a question put by Nadkarni: Let S be an ergodic, conservative and nonsingular automorphism on $(X̃,𝓑_{X̃},m)$. Consider the associated unitary operators on $L²(X̃,𝓑_{X̃},m)$ given by $Ũ_{S}f = √(d(m∘ S)/dm) · (f∘S)$ and $φ·Ũ_{S}$, where φ is a cocycle of modulus one. Does spectral isomorphism of these two operators imply that φ is a coboundary? To answer it negatively, we give an example which arises from an infinite measure-preserving transformation with countable Lebesgue spectrum.

201-204

wydano
2008

### Twórcy

autor
• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
autor
• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland