A note on the range of generalized derivation

Autores: Mohamed Amouch
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 21, Nº 2, 2006, págs. 149-158
Idioma: inglés
Títulos paralelos:
- Nota sobre la imagen de la derivación generalizada
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Resumen
- Let L(H) denote the algebra of bounded linear operators on a complex separable and infinite dimensional Hilbert space H. For A, B Î L(H), the generalized derivation dA,B associated with (A, B), is defined by dA,B(X) = AX - XB for X Î 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 dA,B respect to the given topology and the kernel of dA*,B* vanishes.