Uniformly complete quotient space 𝑈𝐶𝑄(𝐺) and completely isometric representations of 𝑈𝐶𝑄(𝐺)* on ℬ(ℒ₂(𝒢))

Popa, Ana-Maria; Ruan, Zhong-Jin

doi:10.1090/S0002-9939-05-08075-5

Uniformly complete quotient space $UCQ(G)$ and completely isometric representations of $UCQ(G)^*$ on $\mathcal {B}(L_2(G))$
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by Ana-Maria Popa and Zhong-Jin Ruan PDF

Proc. Amer. Math. Soc. 134 (2006), 1223-1235 Request permission

Abstract:

The uniformly complete quotient space $UCQ(G)$ of a locally compact group $G$ is introduced. It is shown that the operator space dual $UCQ(G)^*$ is a completely contractive Banach algebra, which contains the completely bounded Fourier multiplier algebra $M_{cb}A(G)$ as a completely contractively complemented Banach subalgebra. A natural completely isometric representation of $UCQ(G)^*$ on $\mathcal {B}(L_2(G))$ is studied and some equivalent amenability conditions associated with $UCQ(G)$ are proved.

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