Rotund Gâteaux smooth norms which are not locally uniformly rotund
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Publication:6203201
DOI10.1090/proc/16659arXiv2303.01833OpenAlexW4386708676MaRDI QIDQ6203201
Carlo Alberto De Bernardi, Jacopo Somaglia
Publication date: 27 February 2024
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2303.01833
Geometry and structure of normed linear spaces (46B20) Isomorphic theory (including renorming) of Banach spaces (46B03) Convex sets in topological vector spaces (aspects of convex geometry) (52A07)
Cites Work
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- On a property of the norm which is close to locally uniform rotundity
- Inner characterizations of weakly compactly generated Banach spaces and their relatives
- Hilbert generated Banach spaces need not have a norming Markushevich basis
- Uniformly convex renormings and generalized cotypes
- Characterizations of weakly \(\mathcal{K} \)-analytic and Vašák spaces using projectional skeletons and separable PRI
- An Asplund space with norming Markuševič basis that is not weakly compactly generated
- Smooth norms in dense subspaces of Banach spaces
- Banach space theory. The basis for linear and nonlinear analysis
- Convex sets in linear spaces
- Characterizations of Denting Points
- M-Ideals, The Strong 2-Ball Property and Some Renorming Theorems
- Renormings in Banach Spaces
- Projectional skeletons and Markushevich bases
- 𝐶^{𝑘}-smooth approximations of LUR norms
- Some questions about rotundity and renormings in Banach spaces
- Biorthogonal systems in Banach spaces
- Some properties related to nested sequences of balls in Banach spaces
- Renormings preserving local geometry at countably many points in spheres of Banach spaces and applications
- Smooth and Polyhedral Norms via Fundamental Biorthogonal Systems