Norms of elementary operators

作者：Du Hong Ke^*; Wang Yue Qing; Gao Gui Bao

来源：Proceedings of the American Mathematical Society, 2008, 136(4): 1337-1348.

• elementary operator
• norm-attainability
• unitary

Let A(i) and B-i, 1 <= i <= n, be bounded linear operators acting on a separable Hilbert space H. In this note, we prove thats up{parallel to Sigma(n)(i=1)parallel to A(i)XB(i)parallel to : X epsilon B(H), parallel to X parallel to <= 1} = sup{parallel to Sigma(n)(i=1) A(i)UB(i)parallel to : UU* = U*U = I, U epsilon B(H)}. Moreover, we prove that there exists an operator X-0 with parallel to X-0 parallel to = 1 such that parallel to Sigma(n)(i=1)A(i)X(0)B(i)parallel to = sup{parallel to Sigma(n)(i=1)A(i)XB(i)parallel to : X epsilon B(H), parallel to X parallel to <= 1} if and only if there exists a unitary U-0 epsilon B(H) such that parallel to Sigma(n)(i=1) A(i)U(0)B(i)parallel to = sup{parallel to Sigma(n)(i=1) A(i)XB(i)parallel to : X epsilon B(H), parallel to X parallel to <= 1}.

• 出版日期2008
• 单位陕西师范大学