Radial Schur multipliers on some generalisations of trees
Volume 249 / 2019
Studia Mathematica 249 (2019), 59-109
MSC: Primary 46L07; Secondary 05C63, 47B10, 47B35, 30H25.
DOI: 10.4064/sm180424-23-7
Published online: 22 February 2019
Abstract
We give a characterisation of radial Schur multipliers on finite products of trees. The equivalent condition is that a certain generalised Hankel matrix involving the discrete derivatives of the radial function is a trace class operator. This extends Haagerup, Steenstrup and Szwarc’s result for trees. The same condition can be expressed in terms of Besov spaces on the torus. We also prove a similar result for products of hyperbolic graphs, and provide a sufficient condition for a function to define a radial Schur multiplier on a finite-dimensional CAT(0) cube complex.
