Weak-local triple derivations on C*-algebras and JB*-triples

作者：Burgos Maria J; Carlos Cabello Juan; Peralta Antonio M^*

来源：Linear Algebra and Its Applications, 2016, 506: 614-627.

DOI：10.1016/j.laa.2016.06.042

• C*-algebra
• JB*-triple
• Triple derivation
• Weak-local triple derivation
• Weak-local derivation

We prove that every weak-local triple derivation on a JB*-triple E (i.e. a linear map T : E -> E such that for each phi is an element of E* and each a is an element of E, there exists a triple derivation delta(a,phi) : E -> E, depending on phi and a, such that phi T(a) = phi delta(a,phi)(a)) is a (continuous) triple derivation. We also prove that conditions
(h1) {a,T(b),c} = 0 for every a, b, c in E with a, c perpendicular to b; (h2) P-2(e)T(a) = -Q(e)T(a) for every norm-one element a in E, and every tripotent e in E** such that e <= s(a) in E-2**(e), where s(a) is the support tripotent of a in E**,
are necessary and sufficient to show that a linear map T on a JB*-triple E is a triple derivation.

• 出版日期2016-10-1