Compact perturbations of Fredholm 𝑛-tuples

Gelca, Răzvan

doi:10.1090/S0002-9939-1994-1201803-3

Compact perturbations of Fredholm $n$-tuples
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Proc. Amer. Math. Soc. 122 (1994), 195-198 Request permission

Abstract:

Let T be an operator on a Hilbert space. We show that the pair (T, T) can be perturbed to an invertible pair if and only if T is Fredholm of index zero. We also exhibit a large class of Fredholm n-tuples acting on a Banach space which cannot be perturbed by finite rank operators to invertible ones.

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