Commutator criteria for strong mixing II. More general and simpler

  • S. Richard Graduate school of mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan.
  • R. Tiedra de Aldecoa Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile.
Keywords: Strong mixing, unitary representations, commutator methods

Abstract

We present a new criterion, based on commutator methods, for the strong mixing property of unitary representations of topological groups equipped with a proper length function. Our result generalises and unifies recent results on the strong mixing property of discrete flows {Uᴺ}N∈ℤ and continuous flows {e-itH}t∈ℝ induced by unitary operators U and self-adjoint operators H in a Hilbert space. As an application, we present a short alternative proof (not using convolutions) of the strong mixing property of the left regular representation of σ-compact locally compact groups.

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Published
2019-08-14
How to Cite
Richard, S., & Tiedra de Aldecoa, R. (2019). Commutator criteria for strong mixing II. More general and simpler. CUBO, A Mathematical Journal, 21(1), 37–48. https://doi.org/10.4067/S0719-06462019000100037