Closed Ideals, Point Derivations and Weak Amenability of Extended Little Lipschitz Algebras

The structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras

Let $(X,d)$ be a compactmetric space and let $K$ be a nonempty compact subset of $X$. Let $alpha in (0, 1]$ and let ${rm Lip}(X,K,d^ alpha)$ denote the Banach algebra of all  continuous complex-valued functions $f$ on$X$ for which$$p_{(K,d^alpha)}(f)=sup{frac{|f(x)-f(y)|}{d^alpha(x,y)} : x,yin K , xneq y}

Derivations on dual triangular Banach algebras

Ideal Connes-amenability of dual Banach algebras was investigated in [17] by A. Minapoor, A. Bodaghi and D. Ebrahimi Bagha. They studied weak∗continuous derivations from dual Banach algebras into their weak∗-closed two- sided ideals. This work considers weak∗-continuous derivations of dual triangular Banach algebras into their weak∗-closed two- sided ideals . We investigate when weak∗continuous...

ACTA UNIVERSITATIS APULENSIS No 18/2009 AMENABILITY AND WEAK AMENABILITY OF LIPSCHITZ OPERATORS ALGEBRAS

In a recent paper by H.X. Cao, J.H. Zhang and Z.B. Xu a α-Lipschitz operator from a compact metric space into a Banach space A is defined and characterized in a natural way in the sence that F : K → A is a α-Lipschitz operator if and only if for each σ ∈ X∗ the mapping σoF is a α-Lipschitz function. The Lipschitz operators algebras L(K,A) and l(K,A) are developed here further, and we study thei...

Amenability and Weak Amenability of Triangular Banach Algebras

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 ...

Derivations into Duals of Closed Ideals of Banach Algebras

Let A be a Banach algebra. We study those closed ideals I of A for which the first cohomology group of A with coefficients in I is trivial; i.e. H(A, I) = {0}. We investigate such closed ideals when A is weakly amenable or biflat. Also we give some hereditary properties of ideal amenability.