*-标准算子代数上的保半正交可乘映射

Multiplicative maps preserving semi-orthogonality on *-standard operator algebras

研究*-标准算子代数上的双边保半正交映射。刻画作用在无限维Hilbert空间上的*-标准算子代数A上双边保半正交的满射,结果表明:这样的φ具有形式φ(T)=UTV,对任意T∈A成立,其中U,V:H→H是有界线性或共轭线性可逆算子,且U*U=c I,c是非零正实数。

Bilateral semi-orthogonality preserving multiplicative maps on ＊- standard operator algebras are characterized. Bilateral surjeetions preserving semi-orthogonality on ＊ - standard operator algebras o- ver infinite dimensional Hilbert spaces are characterized, and it is shown that such maps have the form φ（T） = UTV ,A↓ T ∈ A , where U, V： H→Hare invertible linear or eonjugate linear bounded operators with U＊ U = cI for some nonzero real constant c.