Algebras of Multilinear Forms on Groups
نویسندگان
چکیده
For locally compact groups Gi, i = 1, 2, · · · , n, let CB(G1, · · · , Gn) denote the Banach space of completely bounded multilinear forms on C0(G1)×· · ·×C0(Gn) in the completely bounded norm. CB(G1, · · · , Gn) has the structure of a Banach ∗-algebra under a multiplication and adjoint operation which agree with the convolution structure on the measure algebra M(G1 ×· · ·×Gn). If the Gi are all abelian, CB(G1, · · · , Gn) carries a naturally defined Fourier transform which generalizes the Fourier-Stieltjes transform on measure algebras. Various other aspects of CB(G1, · · · , Gn) are investigated.
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