Rank-1 nilpotency linear preservers on nest algebras

Let N and M be two nests on Banach spaces X and Y, respectively, and let Phi be a linear map between nest algebras Alg N and Alg M of which the range contains all rank-1 nilpotent operators in Alg M. We give some structure theorems for Phi to be rank-1 nilpotency preserving in both directions, and obtain particularly a characterization of such Phi if it is bounded and X and Y are Hilbert spaces with dim X greater than or equal to 6. (C) 2003 Elsevier Inc. All rights reserved.Mathematics, AppliedMathematicsSCI(E)EI2ARTICLE1-3267-29037