Research Article

Nonlinear maps preserving semi-Fredholm operators with bounded nullity

Published in: Quaestiones Mathematicae
Volume 46 , issue 7 , 2023 , pages: 1415–1421

DOI: 10.2989/16073606.2022.2073572

Author(s): Guoxing Ji Shaanxi Normal University, People’s Republic of China , Xia Jiao Shaanxi Normal University, People’s Republic of China , Weijuan Shi Shaanxi Normal University, People’s Republic of China

Keywords: Primary: 47B48 , Secondary: 15A86 , 47A53 , Preserver , semi-Fredholm operator , nullity

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Abstract

Let be an infinite dimensional complex Banach space, and let be the algebra of all bounded linear operators on . In this paper, given any positive integer n, we provide a characterization of all bijective maps on preserving the diﬀerence of semi-Fredholm operators with nullity less than n, and describe completely the structure of these maps.

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