On Toeplitz algebras of product systems
| dc.contributor.author | Katsoulis, Elias G. | |
| dc.contributor.author | Laca, Marcelo | |
| dc.contributor.author | Sehnem, Camila F. | |
| dc.date.accessioned | 2026-06-25T20:49:57Z | |
| dc.date.available | 2026-06-25T20:49:57Z | |
| dc.date.issued | 2025 | |
| dc.description.abstract | In the setting of product systems over group-embeddable monoids, we consider nuclearity of the associated Toeplitz C*-algebra in relation to nuclearity of the coefficient algebra. Our work goes beyond the known cases of single correspondences and compactly aligned product systems over right least common multiple (LCM) monoids. Specifically, given a product system over a submonoid of a group, we show, under technical assumptions, that the fixed-point algebra of the gauge action is nuclear if and only if the coefficient algebra is nuclear; when the group is amenable, we conclude that this happens if and only if the Toeplitz algebra itself is nuclear. Our main results imply that nuclearity of the Toeplitz algebra is equivalent to nuclearity of the coefficient algebra for every full product system of Hilbert bimodules over abelian monoids, over ax + b-monoids of integral domains and over Baumslag–Solitar monoids BS+(m, n) that admit an amenable embedding, which we provide for m and n relatively prime. | |
| dc.description.reviewstatus | Reviewed | |
| dc.description.scholarlevel | Faculty | |
| dc.description.sponsorship | Part of this work was carried out in person around the International Workshop on Operator Theory and its Applications IWOTA 2022. Elias Katsoulis was partially supported by NSF Grant 2054781 and Marcelo Laca was supported by NSERC Discovery Grant RGPIN-2023-05410. | |
| dc.identifier.citation | Katsoulis, E. G., Laca, M., & Sehnem, C. F. (2025). On Toeplitz algebras of product systems. Journal of the Australian Mathematical Society, 119(3), 436–463. https://doi.org/doi:10.1017/S1446788725101146 | |
| dc.identifier.uri | https://doi.org/doi:10.1017/S1446788725101146 | |
| dc.identifier.uri | https://hdl.handle.net/1828/24017 | |
| dc.language.iso | en | |
| dc.publisher | Journal of the Australian Mathematical Society | |
| dc.rights | Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Toeplitz algebra | |
| dc.subject | product systems | |
| dc.subject | nuclearity | |
| dc.subject.department | Department of Mathematics and Statistics | |
| dc.title | On Toeplitz algebras of product systems | |
| dc.type | Article |