Marcoux, LaurentRadjavi, HeydarRosenthal, Peter2024-01-312024-01-312023https://doi.org/10.1090/proc/16159http://hdl.handle.net/10012/20319First published in the Proceedings of the American Mathematical Society in 151 (2023), published by the American Mathematical Society. https://doi.org/10.1090/proc/16159We consider the question of whether every collection of compact operators that is contained in a triangular operator algebra (in the sense of Kadison and Singer) must be simultaneously triangularisable. The answer is shown to be affirmative if the collection consists of finite-rank operators or is a norm-closed algebra of compact operators.enAttribution-NonCommercial-NoDerivatives 4.0 Internationaltriangular algebrassimultaneous triangularisabilityirreducible algebracompact operatorsArticle