For a scalar λ, two operators T and S are said to λ-commute if TS = λST. In this note we explore the pervasiveness of the operators that λ-commute with a compact operator by characterizing the closure and the interior of the set of operators with this property.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-1, author = {John B. Conway and Gabriel Pr\v ajitur\v a}, title = {On $\lambda$-commuting operators}, journal = {Studia Mathematica}, volume = {166}, year = {2005}, pages = {1-9}, zbl = {1084.47014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-1} }
John B. Conway; Gabriel Prǎjiturǎ. On λ-commuting operators. Studia Mathematica, Tome 166 (2005) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-1/