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STABILITY OF NON-INVERTIBLE OPERATORS ON BANACH SPACES

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Author(s):
Lenarduzzi, Fernando ; Messaoudi, Ali
Total Authors: 2
Document type: Journal article
Source: Proceedings of the American Mathematical Society; v. 153, n. 9, p. 14-pg., 2025-09-01.
Abstract

Let X be a Banach space and T : X -> X be a non-invertible linear continuous map. In this paper, we prove that if T has a right continuous operator inverse R with spectral radius r(R) < 1, then T is strongly Lipschitz structurally stable. We also prove that, if T with spectral radius r(T) < 1 has a left inverse operator, then T is strongly Lipschitz topologically stable. (AU)

FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants