On symmetricity of orthogonality in function spaces and space of operators on Banach spaces
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| Format: | Preprint |
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2025
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| _version_ | 1866915249985159168 |
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| author | Sohel, Shamim Sain, Debmalya Paul, Kallol |
| author_facet | Sohel, Shamim Sain, Debmalya Paul, Kallol |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_13663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On symmetricity of orthogonality in function spaces and space of operators on Banach spaces Sohel, Shamim Sain, Debmalya Paul, Kallol Functional Analysis Primary 47L05, Secondary 46B20 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. |
| title | On symmetricity of orthogonality in function spaces and space of operators on Banach spaces |
| topic | Functional Analysis Primary 47L05, Secondary 46B20 |
| url | https://arxiv.org/abs/2504.13663 |