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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Compact perturbations of Fredholm $ n$-tuples


Author: Răzvan Gelca
Journal: Proc. Amer. Math. Soc. 122 (1994), 195-198
MSC: Primary 47A53; Secondary 47A13, 47A55
MathSciNet review: 1201803
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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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DOI: https://doi.org/10.1090/S0002-9939-1994-1201803-3
Keywords: Fredholm n-tuple, compact perturbation, index zero
Article copyright: © Copyright 1994 American Mathematical Society