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

• Autorzy: K. Frączek , M. Wysokińska
• Języki publikacji: 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.

Kategorie tematyczne

• 37A30: Ergodic theorems, spectral theory, Markov operators
• 37A40: Nonsingular (and infinite-measure preserving) transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 110
• Numer: 1
• Strony: 201-204

Daty

wydano

2008

Twórcy

autor

K. Frączek

• 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

M. Wysokińska

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/cm110-1-8