两个Hilbert Schmidt不等式(英文)

Two Hilbert Schmidt Operator Equalities

设A和B是Hilbert Schmidt算子,U(H)是希尔伯特空间H上酉算子的全体.本文推广了两个矩阵的迹等式,对Hilbert Schmidt算子获得了相应的结论,给出了trAB,sup{‖A—UB‖_2:U∈U(H)}和inf{‖A—UB‖_2:U∈U(H)}的表示.

Let A and B be Hilbert Schmidt operators and U（H） be the set of unitary operators on H. In this note, we generalize two equalities about the trace of matrix to Hilbert Schmidt operators. The explicit representation of trAB, sup{HA-UB｜｜2：U∈U（H）） and inf{｜｜A-UB｜｜2：U∈U（H）） are given.