Let L(H) denote the algebra of bounded linear operators on a complex separable and infinite dimensional Hilbert space H. For A, B ∈ L(H), the generalized derivation δA,B associated with (A, B), is defined by δA,B(X) = AX - XB for X ∈ L(H). In this note we give some sufficient conditions for A and B under which the intersection between the closure of the range of δA,B respect to the given topology and the kernel of δA*,B* vanishes.
@article{urn:eudml:doc:41855,
title = {A note on the range of generalized derivation.},
journal = {Extracta Mathematicae},
volume = {21},
year = {2006},
pages = {149-157},
zbl = {1134.47026},
mrnumber = {MR2292744},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41855}
}
Amouch, Mohamed. A note on the range of generalized derivation.. Extracta Mathematicae, Tome 21 (2006) pp. 149-157. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41855/