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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya // Archive

Funktsional. Anal. i Prilozhen., 2022 Volume 56, Issue 3, Pages 88–92 (Mi faa3986)

This article is cited in 2 papers

Brief communications

Absolute continuity and singularity of spectra for the flows $T_t\otimes T_{at}$

V. V. Ryzhikov

Lomonosov Moscow State University

Abstract: Given disjoint countable dense subsets $C$ and $D$ of the half-line $(1,+\infty)$, there exists a flow $T_t$ preserving a sigma-finite measure and such that all automorphisms $T_1\otimes T_{c}$ with $c\in C$ have simple singular spectrum and all automorphisms $T_1\otimes T_{d}$ with $d\in D$ have Lebesgue spectrum of countable multiplicity.

Keywords: tensor product of flows, absolutely continuous singular spectrum, dissipativity, weak limits of operators.

UDC: 517.987

Received: 18.02.2022
Revised: 27.04.2022
Accepted: 05.05.2022

DOI: 10.4213/faa3986


 English version:
Functional Analysis and Its Applications, 2022, 56:3, 225–228

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© Steklov Math. Inst. of RAS, 2024