Fra\"iss\'e limits in functional analysis

TL;DR

This paper develops a unified framework for Fra"issé limits in functional analysis, covering classical and noncommutative structures like the Gurarij space and Poulsen simplex, and introduces new noncommutative analogs.

Contribution

It provides a comprehensive approach to Fra"issé limits in functional analysis, including new noncommutative analogs of classical structures and universal operators.

Findings

Unified framework for Fra"issé limits in functional analysis

Construction of noncommutative analogs of classical structures

New results on universal operators in noncommutative settings

Abstract

We provide a unified approach to Fra\"{\i}ss\'{e} limits in functional analysis, including the Gurarij space, the Poulsen simplex, and their noncommutative analogs. We obtain in this general framework many known and new results about the Gurarij space and the Poulsen simplex, and at the same time establish their noncommutative analogs. Particularly, we construct noncommutative analogs of universal operators in the sense of Rota.