Additive maps preserving similarity or asymptotic similarity on B(H)

作者：Du Shuanping; Hou Jinchuan^*; Bai Zhaofang

来源：Linear and Multilinear Algebra, 2007, 55(3): 209-218.

DOI：10.1080/03081080500380462

• similarity
• asymptotic similarity
• asymptotic similarity-preserving additive maps

Let H be an infinite-dimensional complex separable Hilbert space and B(H) denote the algebra of all bounded linear operators acting on H. We show that an additive continuous surjective map phi on B(H) is asymptotic similarity preserving if and only if it is similarity preserving, and in turn, if and only if there exist a scalar c and an invertible bounded linear or conjugate linear operator A on H such that either phi(T) = cATA(-1) for all T or phi(T) = cAT*A(-1) for all T.

• 出版日期2007-5
• 单位山西大学; 厦门大学; 山西师范大学; 太原理工大学