Interpolation sets and the Bohr topology of locally compact groups

Rosenthal's theorem describing those Banach spaces containing no copy of l(1) is extended to topological groups replacing l(1) -basis by interpolation sets in the sense of Hartman and RyllNardzewsky (Colloq. Math. 12 (1964) 23-39). This extension provides a characterization of those locally compact groups containing no interpolation sets and of those locally compact groups which respect compactness, i.e, such that every Bohr compact subset is compact. The approach followed in this paper sheds some light on other questions related to the duality theory of non-Abelian locally compact groups. (C) 2003 Elsevier Inc. All rights reserved.