Approximable WAP- and LUC-interpolation sets

TL;DR

This paper introduces and characterizes approximable interpolation sets for algebras of functions on locally compact groups, focusing on weakly almost periodic and uniformly continuous functions, unifying existing concepts.

Contribution

It defines the notion of approximable interpolation sets and provides their characterization in combinatorial and compactification terms, extending prior concepts.

Findings

Characterization of approximable interpolation sets in combinatorial terms

Representation of these sets in terms of $LUC$- and $WAP$-compactifications

Analysis of properties of approximable interpolation sets

Abstract

Extending and unifying concepts extensively used in the literature, we introduce the notion of approximable interpolation sets for algebras of functions on locally compact groups, especially for weakly almost periodic functions and for uniformly continuous functions. We characterize approximable interpolation sets both in combinatorial terms and in terms of the $\mathscr{LUC}$- and $\mathscr{WAP}$-compactifications and analyze some of their properties.