A non-smooth extension of Frechet differentiability of the norm with applications to numerical ranges

DOI10.1017/S0017089500006443zbMath0604.46021OpenAlexW1966446858MaRDI QIDQ3742142

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Publication date: 1986

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0017089500006443

zbMATH Keywords

Fréchet differentiability of the norm at a point in the unit sphere of a Banach spacesemicontinuity of the duality mappingstrong numerical range space

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Numerical range, numerical radius (47A12) General theory of topological algebras (46H05) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (10)

A numerical range characterization of uniformly smooth Banach spaces ⋮ Generic continuity of restricted weak upper semi-continuous set-valued mappings ⋮ Isometric reflections on Banach spaces after a paper of A. Skorik and A. Zaidenberg: ``On isometric reflections in Banach spaces. ⋮ On multiplicatively closed subsets of normed algebras ⋮ On Upper Semicontinuity of Duality Mappings ⋮ Geometrical properties of the product of a \(C^*\)-algebra ⋮ Banach space characterizations of unitaries: a survey ⋮ Weakly open sets in the unit ball of the projective tensor product of Banach spaces ⋮ Absolutely proximinal subspaces of Banach spaces ⋮ Unnamed Item

Cites Work

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• On normed Jordan algebras which are Banach dual spaces
• Noncommutative Jordan C*-algebras
• Geometry of Banach spaces. Selected topics
• Geometrical implications of upper semi-continuity of the duality mapping on a Banach space
• Some extremal problems in the theory of numerical ranges
• Non-Associative Normed Algebras Spanned by Hermitian Elements
• A Vidav-Palmer Theorem for Jordan C∗-Algebras and Related Topics
• The Numerical Range in Banach Algebras and Complex Functions of Exponential type

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