On Generalized Derivations of Fields

Generalized Derivations on Modules

2 00 9 Hardy type derivations on generalized series fields ∗

We consider the valued field K := R((Γ)) of generalized series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a deriva...

Generalized Derivations on Modules *

Let A be a Banach algebra and M be a Banach left A-module. A linear map δ : M → M is called a generalized derivation if there exists a derivation d : A → A such that δ(ax) = aδ(x) + d(a)x (a ∈ A,x ∈ M). In this paper, we associate a triangular Banach algebra T to Banach A-module M and investigate the relation between generalized derivations on M and derivations on T . In particular, we prove th...

On generalized series fields and exponential-logarithmic series fields with derivations.∗

We survey some important properties of fields of generalized series and of exponential-logarithmic series, with particular emphasis on their possible differential structure, based on a joint work of the author with S. Kuhlmann [KM12b, KM11].

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.