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Journal of Operator Theory

Volume 86, Issue 1, Summer 2021  pp. 51-60.

On the isometrisability of group representations on p-spaces

Authors:  Maria Gerasimova (1), Andreas Thom (2)
Author institution: (1) Department of Mathematics, Bar-Ilan University, Ramat Gan, 52900, Israel
(2) Institut fuer Geometrie, TU Dresden, Dresden, 01069, Germany


Summary: In this note we consider a p-isometrisability property of discrete groups. If p=2 this property is equivalent to the well-studied notion of unitarisability. We prove that amenable groups are p-isometrisable for all p(1,). Conversely, we show that every group containing a non-abelian free subgroup is not p-isometrisable for any p(1,). We also discuss some open questions and possible relations of p-isometrisability with the recently introduced Littlewood exponent Lit(Γ).

DOI: http://dx.doi.org/10.7900/jot.2020jan22.2275
Keywords: unitarisability of groups, Dixmier problem, Banach spaces, p-spaces

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