Geodesic
Some Remarks on Orthogonality of Bounded Linear Operators
Journal of convex analysis, Tome 29 (2022) no. 1, pp. 165-181
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We explore the relation between the orthogonality of bounded linear operators in the space of operators and that of elements in the ground space. To be precise, we study if $T, A \in \mathbb{L}(\mathbb{X}, \mathbb{Y})$ satisfy $T \bot_B A$, then whether there exists $ x \in \mathbb{X} $ such that $Tx\bot_B Ax$ with $\|x\| =1$, $\|Tx\| = \|T\|$, where $\mathbb{X}, \mathbb{Y} $ are normed linear spaces. In this context, we introduce the notion of Property $P_n$ for a Banach space and illustrate its connection with orthogonality of a bounded linear operator between Banach spaces. We further study Property $P_n$ for various polyhedral Banach spaces.
Classification : 46B20, 47L05
Mots-clés : Orthogonality, linear operators, norm attainment, polyhedral Banach spaces 
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     author = {A. Ray and K. Paul and D. Sain and S. Dey},
     title = {Some {Remarks} on {Orthogonality} of {Bounded} {Linear} {Operators}},
     journal = {Journal of convex analysis},
     pages = {165--181},
     year = {2022},
     volume = {29},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a9/}
}
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A. Ray; K. Paul; D. Sain; S. Dey. Some Remarks on Orthogonality of Bounded Linear Operators. Journal of convex analysis, Tome 29 (2022) no. 1, pp. 165-181. http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a9/