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Fredholm theory and space ideals. (English) Zbl 0784.47022

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.

MSC:

47A53 (Semi-) Fredholm operators; index theories
47L20 Operator ideals
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