关键词: 零度, 亏数, 可加映射

Abstract:

Let B(X) and B(Y) be the Banach algebras of all bounded linear operators on infinite dimensional complex Banach spaces X and Y, respectively. It is proved that an additive surjective map φ from B(X) to B(Y) preserves the nullity in both directions if and only if there exists invertible bounded linear or conjugate linear operators U:X→Y and V:Y→X, such that φ(T)=UTV for all T∈B(X). A form for additive surjective maps preserving the deficiency in both directions is also obtained.

Key words: nullity, deficiency, additive maps