Interpolation sets and the size of quotients of fu...
Extreme non-Arens regularity of the group algebra by: Filali, Mahmoud Published: (2018)
Algebraic structure of semigroup compactifications : Pym's and Veech's Theorems and strongly prime points by: Filali, M. Published: (2017)
Almost periodic functionals and finite-dimensional representations by: Filali, M. Published: (2018)
Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions by: Eklund, Ted Published: (2017)
Extrapolation and interpolation in generalized Orlicz spaces by: Cruz-Uribe, David Published: (2018)
Filali, M., Galindo, J. (2017) Interpolation sets and the size of quotients of function spaces on a locally compact group. Transactions of the American Mathematical Society, 369 (1), 575-603. https://doi.org/10.1090/tran6662
Interpolation sets and the size of quotients of function spaces on a locally compact group
Filali, Mahmoud1; Galindo, Jorge2
1Department of Mathematical Sciences, University of Oulu, Oulu, Finland
2Instituto Universitario de Matemáticas y Aplicaciones (IMAC), Universidad Jaume I, E-12071, Castellón, Spain
http://urn.fi/urn:nbn:fi-fe2019040811471
American Mathematical Society, 2017
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 set we introduced and studied recently and unifies the approaches followed by many authors to obtain particular cases.
We find in this way that there is a linear isometric copy of \(\ell _\infty (\kappa )\) in each of the following quotient spaces:
\(\mathscr{WAP}_0(G)/C_0(G)\) whenever \(G\) contains a subset \(X\) that is an \(E\)-set (see the definition in the paper) and \(\kappa =\kappa (X)\) is the minimal number of compact sets required to cover \(X\). In particular, \(\kappa =\kappa (G)\) when \(G\) is an \(SIN\)-group.
\(\mathscr{WAP}(G)/\mathscr {B}(G)\), when \(G\) is any locally compact group and \(\kappa =\kappa (Z(G))\) and \(Z(G)\) is the centre of \(G\), or when \(G\) is either an \(IN\)-group or a nilpotent group and \(\kappa =\kappa (G)\).
\(\mathscr{WAP}_0(G)/\mathscr {B}_0(G)\), when \(G\) and \(\kappa\) are as in the foregoing item.
\(\mathscr{CB}(G)/\mathscr {LUC}(G)\), when \(G\) is any locally compact group that is neither compact nor discrete and \(\kappa =\kappa (G)\).
Transactions of the American Mathematical Society
10.1090/tran6662
OADOI:
https://oadoi.org/10.1090/tran6662
A1 Journal article – refereed
Almost periodic functions
Fourier-Stieltjes algebra
almost periodic compactification
interpolation sets
semigroup compactification
weakly almost periodic
The research of the second author was partially supported by the Spanish Ministry of Science (including FEDER funds), grant MTM2011-23118 and Fundació Caixa Castelló-Bancaixa, grant number P1$⋅$1B2014-35.
© Copyright 2016 American Mathematical Society.