Journal of the London Mathematical Society · 2005 · 21 citations · 0 references
Local DerivationsTopological SemigroupsLinear OperatorEngineeringVariational Analysis‘ Local DerivationsMicrolocal AnalysisApproximately Local DerivationsFunctional AnalysisApproximation TheoryDerivations ’Calculus Of Variation
Certain linear operators from a Banach algebra A into a Banach A-bimodule X, which are called approximately local derivations, are studied. It is shown that when A is a C*-algebra, a Banach algebra generated by idempotents, a semisimple annihilator Banach algebra, or the group algebra of a SIN or a totally disconnected group, bounded approximately local derivations from A into X are derivations. This, in particular, extends a result of B. E. Johnson that ‘local derivations on C*-algebras are derivations’ and provides an alternative proof of it.