Abstract
Let \({\cal X}\) be an infinite-dimensional real or complex Banach space, and \({\cal B}({\cal X})\) the Banach algebra of all bounded linear operators on \({\cal X}\). In this paper, given any non-negative integer n, we characterize the surjective additive maps on \({\cal B}({\cal X})\) preserving Fredholm operators with fixed nullity or defect equal to n in both directions, and describe completely the structure of these maps.
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This research was supported by National Natural Science Foundation of China (11771261, 11701351), Natural Science Basic Research Plan in Shaanxi Province of China (2018JQ1082) and the Fundamental Research Funds for the Central Universities (GK202103007, GK202107014).
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Zhang, R., Shi, W. & Ji, G. Additive Mappings Preserving Fredholm Operators with Fixed Nullity or Defect. Acta Math Sci 41, 1670–1678 (2021). https://doi.org/10.1007/s10473-021-0516-3
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DOI: https://doi.org/10.1007/s10473-021-0516-3