Mustafayev, H. S.2025-05-102025-05-1020140008-43951496-428710.4153/CMB-2012-016-12-s2.0-84892640346https://doi.org/10.4153/CMB-2012-016-1https://hdl.handle.net/20.500.14720/16379Let T be a contraction on a complex, separable, infinite dimensional Hilbert space and let sigma(T) (resp. sigma(e)(T)) be its spectrum (resp. essential spectrum). We assume that T is an essentially isometric operator; that is, I-H - T* T is compact. We show that if D\sigma T(T) not equal phi, then for every f from the disc-algebra sigma(e)( f(T)) = f( sigma(e)(T)), where D is the open unit disc. In addition, if T lies in the class C-0. boolean OR C-.0, then sigma(e)( f(T)) = f( sigma(T) boolean AND Gamma), where Gamma is the unit circle. Some related problems are also discussed.eninfo:eu-repo/semantics/openAccessHilbert SpaceContractionEssentially Isometric Operator(Essential) SpectrumFunctional CalculusArticle571Q3Q3145158WOS:000331418000019