Non-linear traces of Choquet type on AF algebras
Operator Algebras
2026-02-03 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2601.14016,
title = {Non-linear traces of Choquet type on AF algebras},
author = {Ryota Ninomiya},
journal= {arXiv preprint arXiv:2601.14016},
year = {2026}
}
Comments
19 pages