Norms of certain Jordan elementary operators

作者：Zhang Xiaoli; Ji Guoxing^*

来源：Journal of Mathematical Analysis and Applications, 2008, 346(1): 251-254.

DOI：10.1016/j.jmaa.2008.05.067

• Jordan elementary operator
• norm
• numerical range

Let H be a complex Hilbert space and let B(H) denote the algebra of all bounded linear operators on H. For A. B is an element of B(H), the Jordan elementary operator U-A,U-B is defined by U-A,U-B(X) = AXB + BXA, for all X is an element of B(H). In this short note, we discuss the norm of U-A,U-B. We show that if dim H = 2 and parallel to U-A,U- (B)parallel to = parallel to A parallel to parallel to B parallel to, then either AB* or B*A is 0. We give some examples of Jordan elementary operators parallel to U-A,U- (B)parallel to such that parallel to U-A,U- (B)parallel to = parallel to A parallel to parallel to B parallel to but AB* not equal 0 and B*A not equal 0, which answer negatively a question posed by M. Boumazgour in [M. Boumazgour, Norm inequalities for sums of two basic elementary operators, J. Math. Anal. Appl. 342 (2008) 386-393)].

• 出版日期2008-10-1
• 单位陕西师范大学