算子代数上的可加映射(英文)

The Additive Maps on Operator Algebras

设 H是 Hilbert空间 ,X是 Banach空间 ,本文刻画了 B0 ( X)上的保幂零可加映射 ,B( X)上的保谱半径可加映射以及 B( H)上的保零化多项式算子的可加映射和线性映射 ,并给出了 von Neumann代数上保正交性或与运算 |· | k 交换的可加映射的具体形式 .

Let H be a Hilbert space and X a Banach space. In this paper, the additive maps which preserve nilpotent operators or spectral radius on B 0(X) and B(X), respectively, are characterized; the linear maps and additive maps on B(H) which preserve operators annihilated by a polynomial are classified; the forms of additive maps on von Neumann algebras which preserve orthogonality or commuting with |·| k are obtained.