Grad colloquium

Wednesday, May 30, 2012 4:30 pm - 5:30 pm EDT (GMT -04:00)

Elcim Elgun, Pure Mathematics Department, University of Waterloo

"The Construction a West Compactication of Z"

Abstract: Given a locally compact group G, a compact semigroup S is called a semigroup compactication if it contains a dense homomorphic image of G. We study the question of extending continuous bounded functions on G to its various semigroup compactications. In particular we are interested in the largest semigroup compactication of G associated with unitary representations, which we will denote by Ge.
In this talk we will restrict our attention to Z. Our aim is to construct a compact subsemigroup of L1[0; 1] as a closure of Z. The construction depends on an idea of West, which implies that this semigroup is a quotient of Ze. This is a strong indication of the algebraic and topological complexity of Ze.