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

K. Frączek, and M. Wysokińska. "Note on the isomorphism problem for weighted unitary operators associated with a nonsingular automorphism." Colloquium Mathematicae 110.1 (2008): 201-204. <http://eudml.org/doc/284013>.

@article{K2008,
abstract = {We give a negative answer to a question put by Nadkarni: Let S be an ergodic, conservative and nonsingular automorphism on $(X̃,_\{X̃\},m)$. Consider the associated unitary operators on $L²(X̃,_\{X̃\},m)$ 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.},
author = {K. Frączek, M. Wysokińska},
journal = {Colloquium Mathematicae},
keywords = {weighted unitary operators; countable Lebesgue spectrum; cylindrical transformations},
language = {eng},
number = {1},
pages = {201-204},
title = {Note on the isomorphism problem for weighted unitary operators associated with a nonsingular automorphism},
url = {http://eudml.org/doc/284013},
volume = {110},
year = {2008},
}

TY - JOUR
AU - K. Frączek
AU - M. Wysokińska
TI - Note on the isomorphism problem for weighted unitary operators associated with a nonsingular automorphism
JO - Colloquium Mathematicae
PY - 2008
VL - 110
IS - 1
SP - 201
EP - 204
AB - We give a negative answer to a question put by Nadkarni: Let S be an ergodic, conservative and nonsingular automorphism on $(X̃,_{X̃},m)$. Consider the associated unitary operators on $L²(X̃,_{X̃},m)$ 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.
LA - eng
KW - weighted unitary operators; countable Lebesgue spectrum; cylindrical transformations
UR - http://eudml.org/doc/284013
ER -