Uniformly continuous functionals on Banach algebras
We continue our study of derivations, multipliers, weak amenability and Arens regularity of Segal algebras on locally compact groups. We also answer two questions on Arens regularity of the Lebesgue-Fourier algebra left open in our earlier work.
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).
For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that has property (FH) if and only if G has property (T). On...
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