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      Interpolation sets and the size of quotients of function spaces on a locally compact group

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          Abstract

          We devise a fairly general method for estimating the size of quotients between algebras of functions on a locally compact group. This method is based on the concept of interpolation sets and unifies the approaches followed by many authors to obtain particular cases. Among the applications we find, we obtain that the quotients WAP(G)/B(G) (G being a locally compact group in the class [IN] or a nilpotent locally compact group) and CB(G)/LUC(G) (G being any non-compact non-discrete locally compact group) contain a linearly isometric copy of \ell_\infty(\kappa(G)) where \kappa(G) is the compact covering number of G, and WAP(G), B(G) and LUC(G) refer, respectively, to the algebra of weakly almost periodic functions, the uniform closure of the Fourier-Stieltjes algebra and the bounded right uniformly continuous functions.

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          Pseudocompactness and uniform continuity in topological groups

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            On the Second Conjugate Algebra of L 1 (G ) of a Locally Compact Group

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              Topological dynamics

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                Author and article information

                Journal
                18 July 2013
                Article
                1307.4941
                5f9ba253-e1a7-49a8-9f20-108967b59a34

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                22D15, 43A46, 43 A15, 43A60, 54H11
                math.FA

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