# REPRESENTATIONS OF LOCALLY COMPACT GROUPS ON QSLP-SPACES AND A P-ANALOG OF THE FOURIER-STIELTJES ALGEBRA

@article{Runde2004REPRESENTATIONSOL, title={REPRESENTATIONS OF LOCALLY COMPACT GROUPS ON QSLP-SPACES AND A P-ANALOG OF THE FOURIER-STIELTJES ALGEBRA}, author={Volker Runde}, journal={Pacific Journal of Mathematics}, year={2004}, volume={221}, pages={379-397} }

For a locally compact group G and p ∈ (1, oo), we define Bp(G) to be the space of all coefficient functions of isometric representations of G on quotients of subspaces of L p spaces. For p = 2, this is the usual Fourier-Stieltjes algebra. We show that Bp(G) is a commutative Banach algebra that contractively (isometrically, if G is amenable) contains the Figa-Talamanca-Herz algebra Ap(G). If 2 ≤ q ≤ p or p ≤ q ≤ 2, we have a contractive inclusion B q (G) ⊂ Bp(G). We also show that Bp(G) embeds…

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