On symmetricity of orthogonality in function spaces and space of operators on Banach spaces
Year: 2025
Type: preprint
Abstract: We study symmetric points with respect to $(ρ_+)$-orthogonality, $(ρ_{-})$-orthogonality and $ρ$-orthogonality in the space $C(K, \mathbb{X}),$ 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 $C(K, \mathbb{X})$ 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.
Source: arXiv (Cornell University)
Authors: Sohel, Shamim, Sain, Debmalya, Paul, Kallol
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979367839
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