×

Perturbation of a Fredholm complex by inessential operators. (English) Zbl 0984.47010

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.

MSC:

47A53 (Semi-) Fredholm operators; index theories
47A13 Several-variable operator theory (spectral, Fredholm, etc.)
47L20 Operator ideals
PDFBibTeX XMLCite
Full Text: EuDML EMIS