The main purpose of this research is to characterize generalized (left) derivations and Jordan (*,*)-derivations on Banach algebras rings using some functional identities. Let A be a unital semiprime algebra let F,G : ? linear mappings satisfying F(x) =-x2G(x-1) for all x Inv(A), where Inv(A) denotes the set invertible elements A. Then both F G are Another result in regard as follows. n > 1 ...

Given a free-by-cyclie group G = FN oφ Z determined by a hyperbolic and fully irreducible outer automorphism φ ∈ Out(FN ), with u0 : G → Z the homomorphism having ker(u0) = FN , we construct a K(G, 1) 2–complex X called the folded mapping torus of φ, and equip it with a semiflow. We show that X enjoys many similar properties to those proven by Thurston and Fried for the mapping torus of a pseud...

1. Statement of results. Let SPW/ e" (0 <p <q) denote the complex obtained by attaching a g-cell e" to the ^-sphere Sp by means of a continuous map/: SQ~l—»Sp. Thus Sp^J/eq is the union of the mapping cylinder of/ with a cone over Sa_1. In this note we consider the problem of imbedding such a complex in euclidean space or, equivalently, in a sphere. It is clear that the mapping cylinder of/ can...

Let A be a C-algebra acting on a Hilbert space H, σ : A → B(H) be a linear mapping and d : A → B(H) be a σ-derivation. Generalizing the celebrated theorem of Sakai, we prove that if σ is a continuous ∗-mapping then d is automatically continuous. In addition, we show the converse is true in the sense that if d is a continuous ∗-σ-derivation then there exists a continuous linear mapping Σ : A → B...

Let A be a C-algebra acting on a Hilbert space H, σ : A → B(H) be a linear mapping and d : A → B(H) be a σ-derivation. Generalizing the celebrated theorem of Sakai, we prove that if σ is a continuous ∗-mapping then d is automatically continuous. In addition, we show the converse is true in the sense that if d is a continuous ∗-σ-derivation then there exists a continuous linear mapping Σ : A → B...