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Norm-parallelism and the Davis--Wielandt radius of Hilbert space operators (1811.00440v1)
Published 1 Nov 2018 in math.FA and math.OA
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.