保不定半正交性的可加映射

设Hi是实或复数域上无限维完备的不定度规空间,Ai是B(Hi)中由单位元I和一个理想生成的子代数,其中B(Hi)表示Hi上所有有界线性算子构成的代数,i=1,2.本文刻画了从A1到A2上双边保不定半正交性的可加满射Ф,即对任意T,S∈A1,T S=0(=)Ф(T) Ф(S)=0.主要结果表明,这样的Ф具有形式Ф(T)=UTV对任意的T∈A1成立,这里U,V是有界线性或共轭线性可逆算子且U U=cI,c是非零实数.

Additive Maps Preserving Indefinite Semi-Orthogonality

Let $H$ be a complete indefinite inner product space of infinite dimension over real or complex field. A characterization of indefinite semi-orthogonality preservingadditive surjection in both directions on unital $\dag$-subalgebras of $\mathcal B(H)$ which contains all finite rank operators is obtained. We show that such maps have the form ${\it \Phi(T)}=UTV$,$\forall T$, where $U$ and $V$ are invertible linear or conjugate linear bounded operators with $UU^\dag =cI$ for some nonzero real constant $c$. As a corollary, semi-orthogonality preserving additive surjections in both directions on unital $\ast$-subalgebra which contains all finite rank operators over Hilbert space are classified.