【摘要】 令N和M分别是实或复Banach空间X(dim X>5)和Y中的两个套且AlgN和AlgM分别是与套N和M相关的套代数．符号AlgFN表示AlgN中所有有限秩算子全体．设Φ:AlgFN→AlgFM是可加映射,且值域包含AlgFM中的所有秩一幂零元．如果Φ-双边保秩一幂零性,作者证明了存在一个域自同构τ及τ-线性算子A和C使得要么对所有的秩一幂零元x(?)f∈AlgFN,Φ(x(?)f)=Ax(?)Cf,要么对所有的秩一幂零元x(?)f∈AlgFN,Φ(x(?)f)=Af(?)Cx．特别地,当X和Y是Hilbert空间且Φ是连续映射时,作者得到这类可加映射Φ的完全刻画．更多还原

【Abstract】 Let N and M be two nests on real or complex Banach spaces X and Y, respectively, andΦbe an additive map between ideals AlgFN and ALGFM of finite rank operators in nest algebras AlgN and AlgM, of which the range contains all rank-1 nilpotent operators in AlgM. The authors show that ifΦis rank-1 nilpotency preserving in both directions, thenΦhas the form eitherΦ(x(?)f) = Ax(?)Cf for every rank-1 nilpotent operator x(?)AlgFN orΦ(x(?)f) = Af(?)Cx for every rank-1 nilpotent operator x(?)f∈AlgFN, where A and C are certainτ-linear operators with an automorphism r of the underlying field. And the authors obtain particularly a characterization of suchΦif it is continuous, X and Y are Hilbert spaces with dimX≥6.更多还原