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Range inclusion results for derivations on noncommutative Banach algebras

Volker Runde (1993)

Studia Mathematica

Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes a result...

Real-linear isometries between certain subspaces of continuous functions

Arya Jamshidi, Fereshteh Sady (2013)

Open Mathematics

In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin...

Reflexivity of the isometry group of some classical spaces.

Félix Cabello Sánchez, Lajos Molnár (2002)

Revista Matemática Iberoamericana

We investigate the reflexivity of the isometry group and the automorphism group of some important metric linear spaces and a1gebras. The paper consists of the following sections: 1. Preliminaries. 2. Sequence spaces. 3. Spaces of measurable functions. Hardy spaces. 5. Banach algebras of holomorphic functions. 6. Fréchet algebras of holomorphic functions. 7. Spaces of continuous functions.

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