Compact perturbations of Fredholm -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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Additional Information

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