Extension of Fourier algebra homomorphisms to duals of algebras of uniformly continuous functionals |
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Authors: | Monica Ilie Ross Stokke |
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Affiliation: | a Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON, Canada, P7B 5E1 b Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, MB, Canada, R3B 2E9 |
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Abstract: | For a locally compact group G, let XG be one of the following introverted subspaces of VN(G): , the C∗-algebra of uniformly continuous functionals on A(G); , the space of weakly almost periodic functionals on A(G); or , the C∗-algebra generated by the left regular representation on the measure algebra of G. We discuss the extension of homomorphisms of (reduced) Fourier-Stieltjes algebras on G and H to cb-norm preserving, weak∗-weak∗-continuous homomorphisms of into , where (XG,XH) is one of the pairs , , or . When G is amenable, these extensions are characterized in terms of piecewise affine maps. |
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Keywords: | Fourier algebra Fourier-Stieltjes algebra Uniformly continuous functionals Introverted subspace Completely bounded maps Piecewise affine maps |
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