Mustafayev, H. S.2025-05-102025-05-1020150017-08951469-509X10.1017/S001708951400055X2-s2.0-84937972659https://doi.org/10.1017/S001708951400055Xhttps://hdl.handle.net/20.500.14720/7738Let A be an invertible operator on a complex Banach space X. For a given alpha >= 0, we define the class D-A(alpha) (Z) (resp. D-A(alpha) (Z(+))) of all bounded linear operators T on X for which there exists a constant C-T > 0, such that parallel to A(n)TA(-n)parallel to <= C-T ( 1 + vertical bar n vertical bar)(alpha), for all n is an element of Z ( resp. n is an element of Z(+)). We present a complete description of the class D-A(alpha) (Z) in the case when the spectrum of A is real or is a singleton. If T is an element of D-A (Z) (= D-A(0) (Z)), some estimates for the norm of AT - TA are obtained. Some results for the class D-A(alpha) (Z(+)) are also given.eninfo:eu-repo/semantics/openAccessArticle573Q4Q3665680WOS:000358484500012