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.
@article{bwmeta1.element.bwnjournal-article-smv109i1p67bwm,
author = {V. Shul'Man},
title = {Operators preserving ideals in C*-algebras},
journal = {Studia Mathematica},
volume = {108},
year = {1994},
pages = {67-72},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv109i1p67bwm}
}
Shul'Man, V. Operators preserving ideals in C*-algebras. Studia Mathematica, Tome 108 (1994) pp. 67-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv109i1p67bwm/
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