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math.FA2026
Surjective maps preserving quasi-nilpotence of products of operators
Zakariae Azna, Fadil Chabbabi
Let be an infinite-dimensional complex Banach space and let the full algebra of all bounded linear operator on . In this paper, we give a complete characteri…
math.FA2026
Algebraic Direct Sums and Generalized Drazin Invertibility
Zakariae Aznay, Fadil Chabbabi
Let be a bounded linear operator on a complex Banach space . We prove that the algebraic decomposition \[ X=\K(T)\oplus \Hq(T) \] forces both summands to be closed and hence…