B(H)上保正交性的可加映射

Additive maps preserving orthogonality on B(H)

讨论了B(H)到B(K)上保反正交性、保Jordan正交性的可加映射,其中B(H)和B(K)是由Hilbert空间H和K上的有界线性算子全体组成的Banach代数.若Φ:B(H)→B(K)是双边保反正交性的可加满射,使得Φ(I)=I,并且对每个一秩幂等算子P∈B(H),有Φ(FP)FΦ(P),则Φ是B(H)上的*-反同构或共轭*-反同构.与保反正交性的假设条件相同,对于保Jordan正交性,得到Φ是下列形式之一:*-同构,共轭*-同构,*-反同构,共轭*-反同构.

It is considered that additive maps preserving anti-orthogonality and preserving Jordan orthogonality between the algebras B（H）and B（H） of all bounded linear operators, acting on the real or the complex Hilbert space B and H Let Φ： B（H）→B（H） be a united additive subjective map preserving anti-orthogonality in both directions, such that Φ （FP）include FΦ（ P ） for all rank one idempotent operators P, then Φ is a ＊- anti-isomorphism or a conjugate ＊- anti-isomorphism; Preserving Jordan orthogonality is characterized under the same assumption as preserving Jordan anti -orthogonality, Φ has one of the following forms： a ＊ -isomorphism, a conjugate ＊ - isomorphism, a ＊ - anti-isomorphism or a conjugate ＊ - anti-isomorphism.