Mustafayev, Heybetkulu2025-05-102025-05-1020150379-40241841-774410.7900/jot.2014jun14.20592-s2.0-84957805238https://doi.org/10.7900/jot.2014jun14.2059https://hdl.handle.net/20.500.14720/7663Let A be an invertible bounded linear operator on a complex Banach space X. With connection to the Deddens algebras, for a given k is an element of N, we define the class D-A(k) of all bounded linear operators T on X for which the conjugation orbits {A(n)TA(-n)}(n is an element of z) satisfies some growth conditions. We present a complete description of the class D-A(k) in the case when the spectrum of A is positive. Individual versions of Katznelson-Tzafriri theorem and their applications to the Deddens algebras are given. The Hille-Yosida space is used to obtain local quantitative results related to the Katznelson-Tzafriri theorem. Some related problems are also discussed.eninfo:eu-repo/semantics/closedAccessOperatorDeddens Algebra(Local) SpectrumEntire FunctionKatznelson-Tzafriri TheoremHille-Yosida SpaceArticle742Q3Q2281306WOS:000370771500002