Derivation ranges
Let \(\delta_A(X)= AX-XA\) be the inner derivation induced by \(A\) on the algebra of bounded operators on a complex separable infinite-dimensional Hilbert space. \textit{J. H. Anderson} [Bull. Am. Math. Soc. 79, 705-708 (1973; Zbl 0269.47021)] and \textit{J. G. Stampfli} [Ill. J. Math. 17, 518-524 (1973; Zbl 0271.47002)] studied the question whether \(I\in\overline{R(\delta_A)}\). Extending some results of Stampfli, the author obtains here sufficient conditions on \(A\) under which \(I\not\in \overline{R(\delta_A)}\).
scientific article; zbMATH DE number 1355337