Abstract
On nonseparable Hilbert spaces there are multiple sets of operators that are analogous to the semi-Fredholm operators on a separable space. We develop the properties of these sets and relate those properties to some recent research. We conclude with a theorem that indicates precisely how far one can go from a given generalized semi-Fredholm operator (or generalized Fredholm operator) and retain the property of generalized semi-Fredholmness (or generalized Fredholmness).
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