Catalog · 10.5281/zenodo.23682412
The noncommutative weak extension principle under OCA
- Martino Lupini · University of Bologna
27 October 2026 · CC BY 4.0 · latest of 2 versions
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The noncommutative weak extension principle under OCA
Martino Lupini
Abstract
We prove that the Open Colouring Axiom implies the noncommutative weak extension principle. Every *-homomorphism between coronas of separable nonunital C*-algebras therefore splits, by a commuting projection, into a part with Borel graph and a part with nonmeagre kernel. This removes Martin's Axiom from Vignati and Yilmaz's theorem and answers their proposed weakening for Theorem A. In particular, all such homomorphisms with stable source are Borel under the Open Colouring Axiom alone. We also obtain Borel product lifts for bounded linear maps between reduced products of separable Banach spaces and separable C*-algebras which respect the canonical coordinate restrictions.
Source repository: https://github.com/eulogica/noncommutative-weak-extension-oca
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BibTeX
@unpublished{Lupini202623682412,
title = {The noncommutative weak extension principle under OCA},
author = {Martino Lupini},
year = {2026},
doi = {10.5281/zenodo.23682412},
note = {Zenodo deposit, latest of 2}
}