Abstract
AbstractWeak amenability of discrete groups was introduced by Haagerup and co‐authors in the 1980s. In particular, weak amenability in known to be stable under taking direct products and free products. In this paper we show that weak amenability (with Cowling–Haagerup constant 1) is stable under taking graph products of discrete groups. Along the way we will construct a wall space associated to the word length structure of a graph product and also give a method of extending completely bounded functions on discrete groups to a completely bounded function on their graph product.
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