Introducing the notions of (inner) σ-derivation, (inner) σ-endomorphism and oneparameter group of σ-endomorphisms (σ-dynamics) on a Banach algebra, we correspond to each σ-dynamics a σ-derivation named as its σ-infinitesimal generator. We show that the σ-infinitesimal generator of a σ-dynamics of inner σ-endomorphisms is an inner σ-derivation and deal with the converse. We also establish a nice...

The aim of this article is to discuss the n-derivation algebras Lie color algebras. It proved that, if base ring contains 1/n-1, L a perfect algebra with zero center, then every triple derivation derivation, and nDer(L)) an inner derivation.

The celebrated Kadison–Sakai theorem states that every derivation on a von Neumann algebra is inner. In this paper, we prove this theorem for ultraweakly continuous ∗-σ-derivations, where σ is an ultraweakly continuous surjective ∗-linear mapping. We decompose a σ-derivation into a sum of an inner σ-derivation and a multiple of a homomorphism. The so-called ∗-(σ, τ)-derivations are also discussed.

the complete 3d nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. for describing the dynamics of the system, the newtonian derivation procedure is followed. the velocity field inside the pipe formulated using hydrostatic and bernoulli equations. the hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...

The complete 3D nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. For describing the dynamics of the system, the Newtonian derivation procedure is followed. The velocity field inside the pipe formulated using hydrostatic and Bernoulli equations. The hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...

The celebrated Kadison-Sakai Theorem states that all derivations on von Neumann algebras are inner. In this paper, we generalize this theorem to the so-called ∗-σderivations where σ is a weakly continuous ∗-linear mapping. We decompose a σ-derivation into a sum of an inner σ-derivation and a multiple of a homomorphism. As a consequence, we establish an extension of the Singer-Wermer Theorem. A ...

This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor algebra of a directed graph. We determine when such a derivation is inner, and describe situations that give rise to non-inner derivations. We also analyze t...

In this paper, we study approximate amenability of matrix algebras. We show that every derivation from Mn(A) into Mn(E) is the sum of an inner derivation and a derivation induced by a derivation from A into E(m), where A is a Banach algebra and E is a Banach A-bimodule. By using this, we provide many results in approximate and permanent weak amenability of these algebras.

We prove that every 2-local derivation from the algebra Mn(A)(n > 2) into its bimodule Mn(M) is a derivation, where A is a unital Banach algebra and M is a unital A-bimodule such that each Jordan derivation from A into M is an inner derivation, and that every 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie d...

let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...