Automatic continuity of derivations onC⁎-algebras andJB⁎-triples

Automatic Continuity of Higher Derivations on JB*-Algebras

automatic continuity of higher derivations on jb*-algebras

Automatic Continuity of Σ - Derivations on C ∗ - Algebras

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...

Continuity of Derivations on //»-algebras

We prove that the separating subspace for a derivation on a nonassociative //'-algebra is contained in the annihilator of the algebra. In particular, derivations on nonassociative H* -algebras with zero annihilator are continuous.

Double Derivations, Higher Double Derivations and Automatic Continuity

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 ...