算子代数上保零积的可加映射(英文)

Additive Maps Preserving Zero-product on Operator Algebras

本文分别刻画了Hilbert空间上自伴算子空间和对称算子空间上双边保零积的可加满射,Hilbert空间上包含单位元和所有有限秩算子的 子代数上双边保半正交性的可加满射,以及vonNeumann代数上,C 代数上和Banach空间标准算子代数上保约当零积的可加或线性满射.

In this paper we give some characterizations of the surjective additive maps on the space of self-product in both directions, the surjective additive maps on the unital *-subalgebras containing all finite rank operators which preserve semi-orthogonality in both directions as well as the surjective additive (or linear) maps on the unital *-subalgebras containing all finite rank operators which preserve semi-orthogonality in both directions as well as the surjective additive (or linerar) maps on such operator algebras as von Neumann algebras, C~*-algebras and standard operator algebras which preserve Jordan zero-product.