Elcim Elgun, Department of Pure Mathematics
"The Eberlein Compactification of Locally Compact Groups"
Given a locally compact group G, the Eberlein compactification Ge is the spectrum of the uniform closure of the Fourier-Stieltjes algebra B(G). It is a semitopological compactification and thus a quotient of the weakly almost periodic compactification Gw. In this talk we aim to study the structure and complexity of Ge. On one hand, for certain Abelian groups, weak∗−closed subsemigroups of L∞[0, 1] may be realized as quotients of Ge, thus showing that Ge is large and complicated in these situations. Conversely, the structures of Ge for certain semidirect product groups show that aspects of the structure of Ge can be quite simple. The levels of complexity of these structures mimic those of Gw, yet many questions about the sizes of their differences remain.