保持幂等算子乘积或约当三乘积非零幂等性的映射(英文)

Maps preserving the idempotency of products or triple Jordan products of idempotent operators

设I(X)是复巴拿赫空间X上幂等算子之全体,其中X的维数至少是3维。本文分别给出了I(X)上双边保持幂等算子乘积和约当三乘积非零幂等性的映射的具体结构形式。

Let I（X） be the set of all idempotent operators on a complex Banach space X.The purpose of this note is to give the concrete form of either that every surjective map φ on I（X） such that AB is a nonzero idempotent if and only if φ（A）φ（B） is for all A,B∈I（X） or that every surjective map φ on I（X） such that ABA is a nonzero idempotent if and only if φ（A）φ（B）φ（A） is for all A,B∈I（X）,when the dimension of X is at least 3.