Ring Derivations on Standard Operator Algebras

Lie Derivations on Banach Algebras

✍ A.R. Villena 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 207 KB

Lie triple derivations on nest algebras

✍ Fangyan Lu 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 102 KB

## Abstract Let __δ__ be a Lie triple derivation from a nest algebra 𝒜 into an 𝒜‐bimodule ℳ︁. We show that if ℳ︁ is a weak\* closed operator algebra containing 𝒜 then there are an element __S__ ∈ ℳ︁ and a linear functional __f__ on 𝒜 such that __δ__ (__A__) = __SA__ – __AS__ + __f__ (__A__)__I__ fo

Inner Derivations on σ-C*-Algebras

✍ N. Christopher Phillips 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 266 KB

We prove the following two improvements of a result of BECKER. (1) If A is a pro-C\*-algebra, then every derivation on A is approximately inner. (2) If A is a separable a-C\*-algebra, and ifevery C\* quotient of A has the property that every derivation on it is inner, then also every derivation on A

A Note on Derivations of Simple Algebras

✍ A. Elduque; F. Montaner 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 319 KB

Necessary and sufficient conditions for all the derivations of a finite dimensional simple nonassociative algebra, over a field of characteristic zero, to be inner are given in terms of the Lie multiplication algebra and the trace of the derivations. 1994 Academic Press, Inc.

On the Simplicity of Lie Algebras of Der

On the Simplicity of Lie Algebras of Derivations of Commutative Algebras

✍ David A. Jordan 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 72 KB

Let R be a commutative algebra over a field k. We prove two related results on the simplicity of Lie algebras acting as derivations of R. If D is both a Lie subalgebra and R-submodule of Der k R such that R is D-simple and either char k = 2 or D is not cyclic as an R-module or D R = R, then we show

Positive Functionals on General Operator

Positive Functionals on General Operator Algebras

✍ V. Lomonosov 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 57 KB

We show that any weakly closed algebra of bounded operators acting on a Banach space and different from the algebra of all bounded operators admits positive vector-functionals continuous in the essential operator norm. ᮊ 2000