Maximal Amenability with Asymptotic Orthogonality in Amalgamated Free Products

TL;DR

This paper demonstrates maximal amenability in certain amalgamated free product von Neumann algebras using Popa's asymptotic orthogonality technique, extending previous methods in the field.

Contribution

It applies Popa's classical asymptotic orthogonality technique to establish maximal amenability in a new class of amalgamated free product von Neumann algebras.

Findings

Maximal amenability established for specific amalgamated free products

Popa's technique effective in this new context

Extends understanding of von Neumann algebra properties

Abstract

We investigate the use of Popa's asymptotic orthogonality to establish maximal amenability for amalgamated free product von Neumann algebras. Although new techniques have recently been developed to consider amalgamated free products, we find that the technique developed by Popa in the 1980s can be used to demonstrate maximal amenability for a certain family of amalgamated free product von Neumann algebras.