González, Manuel; Martinón, Antonio Fredholm theory and space ideals. (English) Zbl 0784.47022 Boll. Unione Mat. Ital., VII. Ser., B 7, No. 2, 473-488 (1993). Generalizations of the classes \(SF_ +\) and \(SF_ -\) of upper and lower semi-Fredholm operators are introduced. \(SF_ +\) and \(SF\) are semigroups which are open, that is they are stable under small norm perturbations. The notation \(F\) denotes the finite dimensionality properties of \(SF_ +\) and \(SF_ -\) and the generalization constructs \(SA_ +\) and \(SA_ - \) for a space ideal \(A\) which is a class of Banach spaces bigger than \(F\).Theorem 3.5 establishes that \(SA_ +\) and \(SA_ -\) are open semigroups with \[ SF_ +\subset SA_ +\quad\text{and}\quad SF_ -\subset SA_ - . \] {} Clear examples are given which illustrate the construction. Reviewer: B.Burrows (Stafford) Cited in 2 Documents MSC: 47A53 (Semi-) Fredholm operators; index theories 47L20 Operator ideals Keywords:upper and lower semi-Fredholm operators; small norm perturbations PDFBibTeX XMLCite \textit{M. González} and \textit{A. Martinón}, Boll. Unione Mat. Ital., VII. Ser., B 7, No. 2, 473--488 (1993; Zbl 0784.47022)