| Maps Preserving Semi-Fredholm Operators with Fixed Nullity |
| Received:August 21, 2023 Revised:December 17, 2023 |
| Key Words:
operator algebra adjacency preserver map semi-Fredholm operator
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| Fund Project:Supported by the Natural Science Basic Research Plan in Shaanxi Province (Grant No.2023-JC-YB-050), Overseas Students Science and Technology Activities Project Merit Funding in Shaanxi Province (Grant No.2022-018) and Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No.23JSQ038). |
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| Abstract: |
| Let $\mathcal{X}$ be an infinite-dimensional complex Banach space, and $\mathcal{B}(\mathcal{X})$ the algebra of all bounded linear operators on $\mathcal{X}$. Given an integer $n \geq 1$, we characterize all the bijective maps on $\mathcal{B}(\mathcal{X})$ preserving the difference of semi-Fredholm operators with nullity equal to $n$ in both directions, and establish the structure of the given maps. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.04.012 |
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