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Nonlinear maps preserving Drazin invertible operators of bounded index

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Abstract Given an integer n ≥ 1, we provide a complete description of all bijective bicontinuous maps, on the algebra of all bounded linear operators acting on an infinite-dimensional complex… Click to show full abstract

Abstract Given an integer n ≥ 1, we provide a complete description of all bijective bicontinuous maps, on the algebra of all bounded linear operators acting on an infinite-dimensional complex or real Banach space, that preserve the difference of Drazin invertible operators of index non-greater than n in both directions.

Keywords: index; maps preserving; nonlinear maps; invertible operators; drazin invertible

Journal Title: Quaestiones Mathematicae
Year Published: 2019

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