Schatten-P类算子空间上保距或完全保距映射

摘要

Let H be a complex Hibert space, dim H≥3,C_p (H) the space of Schatten-p class opeators on H and C~(s_p)>(H) the space of self-adjoin: Schatten-p class operators on H. When 1≤p≤+∞ and p≠2,we give a characterization of distance preserving surjective maps for Schatten-p norms on C_p (H) or C~(s_p) (H). As a application,we obtain a characteriaztion of maps preserves distance completely for schatten-p norms on C_p(H). Also the property of distance preserving surjective maps for Hilbert-Schmidt norms is discussed.%设H为复Hilbert空间,dim H≥3,C_p(H)与C~(s_p)(H)分别表示H上的Schattern-p类算子空间及自伴Schattern-p类算子空间.令1≤p≤+∞且P≠2,给出了C_p(H)或C~(s_p)(H)上保距满射的刻画.应用上述结果,得到C_p(H)上完全保距满射的分类.对C_2(H)上的保距映射的性质也进行了讨论.