Interpolation sets and the size of quotients of function spaces on a locally compact group
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Title
Interpolation sets and the size of quotients of function spaces on a locally compact groupDate
2016-03Publisher
American Mathematical SocietyBibliographic citation
FILALI, Mahmoud; GALINDO, Jorge. Interpolation sets and the size of quotients of function spaces on a locally compact group. Transactions of the American Mathematical Society, 2016.Type
info:eu-repo/semantics/articlePublisher version
http://www.ams.org/journals/tran/2017-369-01/S0002-9947-2016-06662-3/home.html#A ...Version
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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 ... [+]
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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Trans. Amer. Math. Soc. 369 (2017)Rights
© Copyright 2016 American Mathematical Society
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