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On the Haagerup inequality and groups acting on A ˜ n -buildings

Alain Valette (1997)

Annales de l'institut Fourier

Let Γ be a group endowed with a length function L , and let E be a linear subspace of C Γ . We say that E satisfies the Haagerup inequality if there exists constants C , s > 0 such that, for any f E , the convolutor norm of f on 2 ( Γ ) is dominated by C times the 2 norm of f ( 1 + L ) s . We show that, for E = C Γ , the Haagerup inequality can be expressed in terms of decay of random walks associated with finitely supported symmetric probability measures on Γ . If L is a word length function on a finitely generated group Γ , we show that,...

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