Abstract
A Hilbert space operator T ∈ B ( H ) may be said to be “consistent in Fredholm and index” provided that for each S ∈ B ( H ) , one of the following cases occurs: (1) T S and S T are Fredholm together and ind ( T S ) = ind ( S T ) = ind ( S ) ; (2) both T S and S T are not Fredholm. The induced spectrum contributes the conditions for the stability of the single-valued extension property under compact perturbations. We characterize those operators for which the single-valued extension property is stable under compact perturbations.
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