Mustafayev, HS2025-05-102025-05-1020060002-993910.1090/S0002-9939-06-08302-X2-s2.0-33748335421https://doi.org/10.1090/S0002-9939-06-08302-Xhttps://hdl.handle.net/20.500.14720/12413Let T be a contraction on a Banach space and AT the Banach algebra generated by T. Let sigma(u)(T) be the unitary spectrum ( i. e., the intersection of sigma(T) with the unit circle) of T. We prove the following theorem of Katznelson-Tzafriri type: If sigma(u)(T) is at most countable, then the Gelfand transform of R is an element of A(T) vanishes on sigma(u)(T) if and only if lim(n ->infinity) parallel to(TR)-R-n parallel to = 0.eninfo:eu-repo/semantics/openAccessContractionBanach AlgebraSpectrumSemisimplicityArticle