2023/11/22 by Toyota, Ryo, Yang, Zhiyuan · 1 citation
#47 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2311.13651
We study an operator-valued generalization of the Haagerup inequality for Gromov hyperbolic groups. In 1978, U. Haagerup showed that if f is a function on the free group \mathbbFr which is supported on the k-sphere Sk=\x∈ \mathbbFr:ℓ(x)=k\, then the operator norm of its left regular representation is bounded by (k+1)‖f‖2. An operator-valued generalization of it was started by U. Haagerup and G. Pisier. One of the most complete form was given by A. Buchholz, where the ℓ2-norm in the original inequality was replaced by k+1 different matrix norms associated to word decompositions (this type of inequality is also called Khintchine-type inequality). We provide a generalization of Buchholz's result for hyperbolic groups.