Speaker: Vergara Ignacio, Universite Claude Bernard-Lyon 1
Time: 18 July, 8:30--9:30, Place: 503 Gewu Buidling
Abstract: Given a set $X$, a Schur multiplier on $X$ is function $\phi:X\times X\to\mathbb{C}$ defining a bounded operator on $\mathcal{B}(\ell_2(X))$ by multiplication of the matrix coefficients: $T=(T_{xy})_{x,y\in X}\mapsto (\phi(x,y)T_{xy})_{x,y\in X}$. In this talk I will focus on the case when $X$ is (the set of vertices of) an infinite graph and the function $\phi$ depends only on the distance between each pair of vertices. Such a function is said to be radial.
For homogeneous trees, Haagerup, Steenstrup and Szwarc gave a characterisation of radial Schur multipliers in terms of certain Hankel matrices associated to the radial functions. I will discuss some extensions of this result to products of trees, products of hyperbolic graphs and CAT(0) cube complexes.
