On local preservation of orthogonality and its application to isometries

DOI10.1016/J.LAA.2024.03.004MaRDI QIDQ6489365

Jayanta Manna, Kallol Paul, Debmalya Sain

Publication date: 21 April 2024

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

isometrylinear operatorsBirkhoff-James orthogonalitypolyhedral Banach spacesfinite-dimensional Banach spaces\(k\)-smoothness

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Isometric theory of Banach spaces (46B04) Linear spaces of operators (47L05) Operators on Banach spaces (47B01)

Cites Work

• Birkhoff-James orthogonality and smoothness of bounded linear operators
• Multismoothness in Banach spaces
• On the norm attainment set of a bounded linear operator and semi-inner-products in normed spaces
• On the numerical index of polyhedral Banach spaces
• Characterization of \(k\)-smooth operators between Banach spaces
• On the norm attainment set of a bounded linear operator
• Multi-smooth points of finite order
• Orthogonality in linear metric spaces
• On maps that preserve orthogonality in normed spaces
• Operators preserving orthogonality are isometries
• $k$-smoothness: an answer to an open problem
• Convex Polyhedra
• Characterization of k-smoothness of operators defined between infinite-dimensional spaces
• $k$-smoothness on polyhedral Banach spaces
• A complete characterization of smoothness in the space of bounded linear operators
• Orthogonality and Linear Functionals in Normed Linear Spaces
• Level numbers of a bounded linear operator between normed linear spaces and singular value decomposition revisited

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