### Uniformly continuous functionals on Banach algebras

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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 ${C}_{c}\left(G\right)$ 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 $({C}_{c}\left(G\right),{\epsilon}_{G})$ has property (FH) if and only if G has property (T). On...

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