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math.FA2025
The Daugavet property is equivalent to the polynomial Daugavet property
Sheldon Dantas, Miguel Martín, Yoël Perreau
In this note, we prove that the Daugavet property implies the polynomial Daugavet property, solving a longstanding open problem in the field. Our approach is based on showing that…
math.FA2024
Twisted Hilbert spaces defined by bi-Lipschitz maps
Willian Corrêa, Sheldon Dantas, Daniel L. Rodríguez-Vidanes
We obtain an infinite-dimensional cone of singular twisted Hilbert spaces which are isomorphic to their duals but not to their conjugate duals. We do that by showing that th…
math.FA2024
Searching for linear structures in the failure of the Stone-Weierstrass theorem
Marc Caballer, Sheldon Dantas, Daniel L. Rodríguez-Vidanes
We investigate the failure of the Stone-Weierstrass theorem focusing on the existence of large dimensional vector spaces within the set $\mathcal{C}(L, \mathbb{K}) \setminus \overl…