Rank-1 nilpotency linear preservers on nest algebras. (Q1418983)

There are several linear preserver problems considered on \(B(H)\) (the algebra of all bounded linear operators acting on the Hilbert space \(H\)) the study of which can be reduced to the study of linear transformations that preserve rank-1 nilpotent operators. In this paper, under certain conditions the authors describe the general form of those transformations when they are defined on nest algebras. We mention that linear preserver problems on nest algebras have been attracting more and more interest in recent years.