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$ q$-Araki-Woods algebras: Extension of second quantisation and Haagerup approximation property


Author: Mateusz Wasilewski
Journal: Proc. Amer. Math. Soc. 145 (2017), 5287-5298
MSC (2010): Primary 46L10
DOI: https://doi.org/10.1090/proc/13681
Published electronically: July 20, 2017
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Abstract: We extend the class of contractions for which the second quantisation on $ q$-Araki-Woods algebras can be defined. As a corollary, we prove that all $ q$-Araki-Woods algebras possess the Haagerup approximation property.


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Mateusz Wasilewski
Affiliation: Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland
Email: mwasilewski@impan.pl

DOI: https://doi.org/10.1090/proc/13681
Received by editor(s): October 12, 2016
Received by editor(s) in revised form: January 18, 2017
Published electronically: July 20, 2017
Additional Notes: The author was partially supported by the NCN (National Centre of Science) grant 2014/14/E/ST1/00525 and acknowledges support by the French MAEDI and MENESR and by the Polish MNiSW through the Polonium programme
Communicated by: Adrian Ioana
Article copyright: © Copyright 2017 American Mathematical Society