Operators preserving ideals in C*-algebras
Volume 109 / 1994
Studia Mathematica 109 (1994), 67-72
DOI: 10.4064/sm-109-1-67-72
Abstract
The aim of this paper is to prove that derivations of a C*-algebra A can be characterized in the space of all linear continuous operators T : A → A by the conditions T(1) = 0, T(L∩R) ⊂ L + R for any closed left ideal L and right ideal R. As a corollary we get an extension of the result of Kadison [5] on local derivations in W*-algebras. Stronger results of this kind are proved under some additional conditions on the cohomologies of A.
