Non-linear traces of Choquet type on AF algebras

We study non-linear traces of Choquet type on AF algebras. Building on the characterization of Choquet traces on matrix algebras due to Nagisa–Watatani, we generalize the construction to arbitrary unital AF algebras. We show that there is a one-to-one correspondence between such traces and increasing functions on the dimension scale, and we obtain explicit Choquet formulas in terms of the spectrum and ranks of spectral projections along a fixed AF filtration.

💡 Research Summary

The paper “Non‑linear traces of Choquet type on AF algebras” extends the notion of Choquet‑type nonlinear traces, originally introduced by Nagisa and Watatani for full matrix algebras, to arbitrary unital approximately finite‑dimensional (AF) C∗‑algebras. The authors begin by recalling the discrete Choquet integral on a finite set, emphasizing its three defining properties: monotonicity, positive homogeneity, and comonotonic additivity. They then abstract these properties to the operator‑algebraic setting, defining a Choquet trace φ : A⁺→