2023/02/21 by Evgenios T. A. Kakariadis, Kakariadis, Evgenios, Elias G. Katsoulis +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2302.10869
openalex publication_date 2023/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Let \A and \B be operator algebras with c0-isomorphic diagonals and let \K denote the compact operators. We show that if \A⊗\K and \B⊗\K are isometrically isomorphic, then \A and \B are isometrically isomorphic. If the algebras \A and \B satisfy an extra analyticity condition a similar result holds with \K being replaced by any operator algebra containing the compact operators. For non-selfadjoint graph algebras this implies that the graph is a complete invariant for various types of isomorphisms, including stable isomorphisms, thus strengthening a recent result of Dor-On, Eilers and Geffen. Similar results are proven for algebras whose diagonals satisfy cancellation and have K0-groups isomorphic to \bbZ. This has implications in the study of stable isomorphisms between various semicrossed products.