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

2018/07/26 by Ali Zamani, Mohammad Sal Moslehian, Mao-Ting Chien +1 · 1 citation
Computer Science · Mathematics · #Matrix Theory and Algorithms #Holomorphic and Operator Theory #Mathematical Inequalities and Applications

paper · doi:10.1080/03081087.2018.1484422

Abstract

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.

Cited by

• Davis-Wielandt radius inequalities for off-diagonal operator matrices

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