On symmetricity of orthogonality in function spaces and space of operators on Banach spaces

2025/04/18 by Sohel, Shamim, Sain, Debmalya, Paul, Kallol
#FOS: Mathematics #Functional Analysis (math.FA) #Primary 47L05 #Secondary 46B20

paper · doi:10.48550/arxiv.2504.13663

Abstract

We study symmetric points with respect to (ρ₊)-orthogonality, (ρ_-)-orthogonality and ρ-orthogonality in the space C(K, \mathbbX), where K is a perfectly normal, compact space and \mathbb X is a Banach space. We characterize left symmetric points and right symmetric points in C(K, \mathbbX) with respect to (ρ₊)-orthogonality and (ρ_-)-orthogonality, separately. Furthermore, we provide necessary conditions for left symmetric and right symmetric points with respect to ρ-orthogonality. As an application of these results we also study these symmetric points in the space of operators defined on some special Banach spaces.

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