Property (T) for Banach algebras

2023/10/27 by Elkiær, Emilie Mai, Pooya, Sanaz · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2310.18136

Abstract

We define and study the notion of property (\rm T) for Banach algebras, generalizing the one from C^*-algebras. For a second countable locally compact group G and a given family of Banach spaces \mathcal E, we prove that our Banach algebraic property (\rmT_{\mathcal E}) of the symmetrized pseudofunction algebras F^*_{\mathcal E}(G) characterizes the Banach property (\rmT_{\mathcal E}) of Bader, Furman, Gelander and Monod for groups. In case G is a discrete group and \mathcal E is the class of L^p-spaces for 1≤ p < ∞, we also achieve the analogue characterization using the symmetrized p-pseudofunction algebras F^*_{λ_ p}(G).

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