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Ultracompanions of subsets of a group

I. Protasov, S. Slobodianiuk (2014)

Commentationes Mathematicae Universitatis Carolinae

Let G be a group, β G be the Stone-Čech compactification of G endowed with the structure of a right topological semigroup and G * = β G G . Given any subset A of G and p G * , we define the p -companion Δ p ( A ) = A * G p of A , and characterize the subsets with finite and discrete ultracompanions.

Unitary closure and Fourier algebra of a topological group

Anthony To-Ming Lau, Jean Ludwig (2015)

Studia Mathematica

This is a sequel to our recent work (2012) on the Fourier-Stieltjes algebra B(G) of a topological group G. We introduce the unitary closure G̅ of G and use it to study the Fourier algebra A(G) of G. We also study operator amenability and fixed point property as well as other related geometric properties for A(G).

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