Norm-parallelism and the Davis-Wielandt radius of Hilbert space operators

作者:Zamani, Ali*; Moslehian, Mohammad Sal; Chien, Mao-Ting; Nakazato, Hiroshi
来源:Linear and Multilinear Algebra, 2019, 67(11): 2147-2158.
DOI:10.1080/03081087.2018.1484422

摘要

We present a necessary and sufficient condition for the norm-parallelism of bounded linear operators on a Hilbert space. We also give a characterization of the Birkhoff-James orthogonality for Hilbert space operators. Moreover, we discuss the connection between norm-parallelism to the identity operator and an equality condition for the Davis-Wielandt radius. Some other related results are also discussed.