Amenability and weak amenability of the Fourier algebra

The amenability constant of the Fourier algebra

For a locally compact group G, let A(G) denote its Fourier algebra and Ĝ its dual object, i.e. the collection of equivalence classes of unitary representations of G. We show that the amenability constant of A(G) is less than or equal to sup{deg(π) : π ∈ Ĝ} and that it is equal to one if and only if G is abelian.

Amenability and Weak Amenability of the Semigroup Algebra l^1 (〖 S〗_T )

Let S be a semigroup with a left multiplier  on S. A new product on S is defined by  related to S and  such that S and the new semigroup ST have the same underlying set as S. It is shown that if  is injective then where, is the extension of  on  Also, we show that if  is bijective then is amenable if and only if is so. Moreover, if  S completely regular, then is weakly amenable. 

Weak amenability of (2N)-th dual of a Banach algebra

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.

Weak Amenability and 2-weak Amenability of Beurling Algebras

Let Lω(G) be a Beurling algebra on a locally compact abelian group G. We look for general conditions on the weight which allows the vanishing of continuous derivations of Lω(G). This leads us to introducing vector-valued Beurling algebras and considering the translation of operators on them. This is then used to connect the augmentation ideal to the behavior of derivation space. We apply these ...

Amenability and Weak Amenability of Triangular Banach Algebras