Stable isomorphisms of operator algebras

Kakariadis, E. T.A., Katsoulis, E. G. and Li, X. (2023) Stable isomorphisms of operator algebras. International Mathematics Research Notices, (doi: 10.1093/imrn/rnad146) (Early Online Publication)

Abstract

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 nonselfadjoint 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 Z. This has implications in the study of stable isomorphisms between various semicrossed products.

• Item Type: Articles
• Additional Information: E. Kakariadis acknowledges support from EPSRC as part of the programme “Operator Algebras for Product Systems” (EP/T02576X/1). E. Katsoulis was partially supported by the NSF grant DMS-2054781. X.L. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 817597).
• Keywords: stable isomorphism, diagonal, semicrossed product, compact operator
• Status: Early Online Publication
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Li, Professor Xin
• Authors: Kakariadis, E. T.A., Katsoulis, E. G., and Li, X.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Mathematics Research Notices
• Publisher: Oxford University Press
• ISSN: 1073-7928
• ISSN (Online): 1687-0247
• Published Online: 31 July 2023
• Copyright Holders: Copyright © The Author(s) 2023
• First Published: First published in International Mathematics Research Notices 2023
• Publisher Policy: Reproduced in accordance with the publisher copyright policy