Stability of non-invertible operators on Banach spaces
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American Mathematical Society (AMS)
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Abstract
Let XX be a Banach space and T:X→XT: X \to X be a non-invertible linear continuous map. In this paper, we prove that if TT has a right continuous operator inverse R with spectral radius r(R)>1r(R)>1, then TT is strongly Lipschitz structurally stable. We also prove that, if TT with spectral radius r(T)>1r(T)>1 has a left inverse operator, then TT is strongly Lipschitz topologically stable.
