Journal of Convex Analysis 27 (2020), No. 3, 881--892
Copyright Heldermann Verlag 2020
Characterization of Approximate Birkhoff-James Orthogonality Sets in a Banach Space
Jeet Sen
Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India
senet.jeet@gmail.com
Arpita Mal
Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India
arpitamalju@gmail.com
Kallol Paul
Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India
kalloldada@gmail.com
There are two notions of approximate Birkhoff-James orthogonality sets in a Banach space. A geometric study of them has recently been done by D. Sain, K. Paul and A. Mal [On approximate Birkhoff-James orthogonality and normal cones in a normed space, J. Convex Analysis 26 (2019) 341--351]. We here characterize completely one of these sets in terms of normal cones. We obtain a uniqueness criterion between approximate orthogonality sets and normal cones in a Banach space. We also investigate the action of a bounded linear operator on approximate Birkhoff-James orthogonality sets.
Keywords: Approximate Birkhoff-James orthogonality, normal cone, smoothness, strictly convex space.
MSC: 46B20; 52A10.
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