Relative discrete spectrum of W*-dynamical systems

TL;DR

This paper introduces a new concept of relative discrete spectrum for noncommutative W*-dynamical systems, connecting it to classical cases, weak mixing, and providing noncommutative examples.

Contribution

It defines the relative discrete spectrum in the noncommutative setting using von Neumann algebra constructions, bridging classical and quantum dynamical systems.

Findings

Defines relative discrete spectrum for W*-dynamical systems

Establishes connections with relative weak mixing

Provides noncommutative examples

Abstract

A definition of relative discrete spectrum of noncommutative W*-dynamical systems is given in terms of the basic construction of von Neumann algebras, motivated from three perspectives: Firstly, as a complementary concept to relative weak mixing of W*-dynamical systems. Secondly, by comparison with the classical (i.e. commutative) case. And, thirdly, by noncommutative examples.