Derivations on Real and Complex Jb*-Triples

Measures of weak non-compactness in preduals of von Neumann algebras and JBW⁎-triples

“…page 16). It is shown in the proof of [38,Proposition 2] that every Cartan factor of type 2 with dim(H) even, or infinite, and every Cartan factor of type 3 contains a unitary element. The same result actually proves that Cartan factors of type 2 with dim(H) even, or infinite, and all Cartan factors of type 3 are JBW * -algebras.…”

A survey on local and 2-local derivations on C*- and von Neuman algebras

“…It is not hard to check that ℜe T (λ 1 , λ 2 )|(λ 1 , λ 2 ) = 0, and thus, Suppose now that δ : E → E is a real linear derivation. Since every real JB * -triple E satisfies the Inner Approximation Property defined in [12,Theorem 4.6] and [38,Theorem 5]) (that is, the space of all inner triple derivations on E is dense in the space of all triple derivations on E, with respect to the strong operator topology of B(E)), given ε > 0 and x ∈ E, there exists a inner derivation δ = n j=1…”

Local Triple Derivations on Real C $$^*$$ ∗ -Algebras and JB $$^*$$ ∗ -Triples

“…Unfortunately, there exist examples of real and complex JB * -triples which do not satisfy the IDP (compare [17]). When the space of all inner triple derivations on E is dense in the space of all triple derivations on E, with respect to the strong operator topology of L(E), we shall say that E has the inner approximation property (IAP for short).…”