The $M_d$-approximation property and unitarisability
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- by Ignacio Vergara;
- Proc. Amer. Math. Soc. 151 (2023), 1209-1220
- DOI: https://doi.org/10.1090/proc/16204
- Published electronically: December 21, 2022
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Abstract:
We define a strengthening of the HaagerupâKraus approximation property by means of the subalgebras of HerzâSchur multipliers $M_d(G)$ ($d\geq 2$) introduced by Pisier. We show that unitarisable groups satisfying this property for all $d\geq 2$ are amenable. Moreover, we show that groups acting properly on finite-dimensional CAT(0) cube complexes satisfy $M_d$-AP for all $d\geq 2$. We also give examples of non-weakly amenable groups satisfying $M_d$-AP for all $d\geq 2$.References
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Bibliographic Information
- Ignacio Vergara
- Affiliation: Saint-Petersburg State University, Leonhard Euler International Mathematical Institute, 14th Line 29B, Vasilyevsky Island, St. Petersburg 199178, Russia
- MR Author ID: 1126379
- ORCID: 0000-0001-7144-4272
- Email: ign.vergara.s@gmail.com
- Received by editor(s): March 11, 2022
- Received by editor(s) in revised form: July 5, 2022
- Published electronically: December 21, 2022
- Additional Notes: This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No. 075-15-2022-287
- Communicated by: Adrian Ioana
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 1209-1220
- MSC (2020): Primary 43A07; Secondary 22D10, 22D12, 46L07, 20F65
- DOI: https://doi.org/10.1090/proc/16204
- MathSciNet review: 4531649