ملخص: Let A [set membership, variant] L(H1), B [set membership, variant] L(H2) (where H1, H2 are Hilbert spaces), and let [delta]A, B denote the operator on L(H2, H1) given by[delta]A, B(X)=AX-XB, X[epsilon]L(H2, H1)J. P. Williams asked: For which A is R([delta]A)t- [intersection] {A*} = {0}? (where [delta]A, A = [delta]A) We obtain some operators in this class. The case of [delta]A, B, A|B, is interesting in itself; moreover it is useful if we have to use a decomposition of the Hilbert space in a direct some for the consideration of [delta]A. In this note we describe some classes of operators A, B for which we have R([delta]A, B - [intersection] ker [delta]A*, B* = {0}.

لغة: فرنسية