Let $\mathcal{X}$ be an infinite-dimensional real or complex Banach space, and $\mathcal{B}(\mathcal{X})$ the Banach algebra of all bounded linear operators on $\mathcal{X}$. In this paper, given any non-negative integer $n$, we characterize the surjective additive maps on $\mathcal{B}(\mathcal{X})$ preserving Fredholm operators with fixed nullity or defect equal to $n$ in both directions, and describe completely the structure of these maps.
Ruihan ZHANG
,
Weijuan SHI
,
Guoxing JI
. ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT[J]. Acta mathematica scientia, Series B, 2021
, 41(5)
: 1670
-1678
.
DOI: 10.1007/s10473-021-0516-3
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