Geodesic
A Topological Generalization of Orthogonality in Banach Spaces and some Applications
Journal of convex analysis, Tome 29 (2022) no. 3, pp. 703-716
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We introduce a topological notion of orthogonality in a vector space. We show that for a suitable choice of orthogonality space, Birkhoff-James orthogonality in a Banach space is a particular case of the orthogonality introduced by us. We characterize the right additivity of orthogonality in our setting and obtain a necessary and sufficient condition for a Banach space to be smooth, as a corollary to our characterization. Finally, using our notion of orthogonality, we obtain a topological generalization of the Bhatia-Semrl Theorem.
Classification : 57N17, 47L05, 46A03
Mots-clés : Vector space with a topology, Birkhoff-James orthogonality, locally convex spaces, Bhatia-Semrl Theorem 
@article{JCA_2022_29_3_JCA_2022_29_3_a2,
     author = {D. Sain and S. Roy and K. Paul},
     title = {A {Topological} {Generalization} of {Orthogonality} in {Banach} {Spaces} and some {Applications}},
     journal = {Journal of convex analysis},
     pages = {703--716},
     year = {2022},
     volume = {29},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_3_JCA_2022_29_3_a2/}
}
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D. Sain; S. Roy; K. Paul. A Topological Generalization of Orthogonality in Banach Spaces and some Applications. Journal of convex analysis, Tome 29 (2022) no. 3, pp. 703-716. http://geodesic.mathdoc.fr/item/JCA_2022_29_3_JCA_2022_29_3_a2/