Relative weak mixing of W$^*$-dynamical systems via joinings

Abstract

A characterization of relative weak mixing in W*dynamical systems in terms of a relatively independent joining is proven.Date: 2017-8-22. 2010 Mathematics Subject Classification. Primary 46L55.

Relative discrete spectrum of W*-dynamical systems

“…As the first step towards the concept of relative discrete spectrum, we study how relatively independent joinings (see [4,2]) can be expressed in terms of the basic construction. Combining this with theory from [5] regarding relative weak mixing, places us in a position to proceed to relative discrete spectrum in the next section.…”

“…In order to motivate our definition of relative discrete spectrum, we are going to make use of ideas from relative weak mixing, as developed in [1, Sections 3 and 4] and [13, Section 2], and subsequently studied further in [5] in connection to relatively independent joinings.…”