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

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Frączek K., Wysokińska M.

Colloquium Mathematicum

2008

tom 110

nr 1

201-204

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Frączek K.

1 Wysokińska M.

1 2008

Wyniki wyszukiwania

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