M_d-multipliers of a locally compact group

2024/08/19 by Battseren, Bat-Od
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2408.09638

Abstract

We show that the space M_d(G) of M_d-multipliers of a locally compact group G is isometrically isomorphic to the Banach space of bounded functionals on the d-fold Haagerup tensor product of L¹(G) vanishing on the kernel of the convolution map. Consequently, we see that M_d(G) is isometrically isomorphic to the dual space of X_d(G), the completion of L¹(G) in the dual of M_d(G). We also show that M_d-type-approximation-properties are inherited to lattices.

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