A. Zamani, M. S. Moslehian, M. T. Chien, H. Nakazato
Published 2018-11-01Version 1
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.
Comments: 11 pages, to appear in Linear Multilinear Algebra
Numerical radius parallelism of Hilbert space operators
A complete characterization of Birkhoff-James orthogonality of bounded linear operators
On some geometric properties of operator spaces
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