Gleason, Jim Perturbation of a Fredholm complex by inessential operators. (English) Zbl 0984.47010 Georgian Math. J. 8, No. 1, 61-67 (2001). Let \({\mathcal B}({\mathcal E},{\mathcal F})\) (resp. \({\mathcal K}({\mathcal E},{\mathcal F})\)) denote the set of all bounded linear operators (resp. all compact operators) from \({\mathcal E}\) to \({\mathcal F}\) for Banach spaces \({\mathcal E}, {\mathcal F}.\) By definition an operator \(S\in {\mathcal B}({\mathcal E},{\mathcal F})\) belongs to the ideal of inessential operators, \({\mathcal P}({\mathcal E},{\mathcal F}),\) if for each \(L\in {\mathcal B}({\mathcal F},{\mathcal E})\) there exist \(U\in {\mathcal B}({\mathcal E},{\mathcal E})\) and \(K\in {\mathcal K}({\mathcal E},{\mathcal E})\) such that \( U(\text{ id}_{{\mathcal E}}-LS)=\text{ id}_{{\mathcal E}}-K.\) The aim of the paper to generalized the Ambrozie-Vasilescu theorem on perturbation of Fredholm complexes by compact operators and to show that a Banach space complex over the complex numbers which is a perturbation of a Fredholm complexes by inessential operators is also Fredholm. Reviewer: V.M.Deundjak (Rostov-na-Donu) MSC: 47A53 (Semi-) Fredholm operators; index theories 47A13 Several-variable operator theory (spectral, Fredholm, etc.) 47L20 Operator ideals Keywords:Fredholm complex; inessential operators; compact perturbation; Ambrozie-Vasilescu theorem PDFBibTeX XMLCite \textit{J. Gleason}, Georgian Math. J. 8, No. 1, 61--67 (2001; Zbl 0984.47010) Full Text: EuDML EMIS