3-L-dendriform algebras and generalized derivations

MODULE GENERALIZED DERIVATIONS ON TRIANGULAUR BANACH ALGEBRAS

Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $A_i$ into the dual space $A^*_i$ (for$i=1,2$) and such derivations  from  the triangular Banach algebraof t...

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

Generalized Derivations and Generalized Amenability of Banach Algebras

Amenability is a cohomological property of Banach algebras which was introduced by Johnson in [14]. Let A be a Banach algebra, and suppose that X is a Banach A−bimodule such that the following statements hold ∥a · x∥ ≤ ∥a∥∥x∥ and ∥x · a∥ ≤ ∥a∥∥x∥ for each a ∈ A and x ∈ X. We can define the right and left actions of A on dual space X∗ of X via ⟨x, λ · a⟩ = ⟨a · x, λ⟩ ⟨x, a · λ⟩ = ⟨x · a, λ⟩, for...

module generalized derivations on triangulaur banach algebras

let $a_1$, $a_2$ be unital banach algebras and $x$ be an $a_1$-$a_2$- module. applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $a_i$ into the dual space $a^*_i$ (for$i=1,2$) and such derivations  from  the triangular banach algebraof t...

On Generalized Left Derivations in BCI-Algebras

In the present paper, we introduce the notion of generalized left derivation of a BCI-algebra X , construct several examples, and investigate related properties. Also establish some results on regular generalized left derivation. Furthermore, for a generalized left derivation H, the concept of a H-invariant generalized left derivation is introduced, and examples are discussed. Using this concep...