DERIVATION AND JORDAN OPERATORS

Authors
SEDDIK A CHARLES J
Citation
A. Seddik et J. Charles, DERIVATION AND JORDAN OPERATORS, Integral equations and operator theory, 28(1), 1997, pp. 120-124
Citations number
4
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics
Journal title
Integral equations and operator theory → ACNP
ISSN journal
0378620X
Volume
28
Issue
1
Year of publication
1997
Pages
120 - 124
Database
ISI
SICI code
0378-620X(1997)28:1<120:DAJO>2.0.ZU;2-H
Abstract
For A is an element of L(H) (the algebra of all operators on the compl ex Hilbert space H), let delta(A) denote the operator on L(H) defined by : delta(A)(X) = AX - XA. We show here that for all Jordan operators A : R(delta(A)) boolean AND {A}' = {0}, where R(delta(A)) is the ran ge of delta(A) and {A}' is the commutant of the adjoint of A.