Work

Twisted Hilbert spaces defined by bi-Lipschitz maps

Year: 2024

Type: preprint

Abstract: We obtain an infinite-dimensional cone of singular twisted Hilbert spaces $Z(φ)$ which are isomorphic to their duals but not to their conjugate duals. We do that by showing that the subset of all bi-Lipschitz maps from $[0, \infty)$ to $\mathbb{R}$ is coneable. We also provide a characterization of the Kalton-Peck space among all twisted Hilbert spaces of the form $Z(φ)$, which gives a partial answer to a conjecture of F. Cabello Sánchez and J. Castillo.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2408.07827

Authors: Corrêa, Willian, Dantas, Sheldon, Rodríguez-Vidanes, Daniel L.

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Generalitat Valenciana, Conselho Nacional de Desenvolvimento Científico e Tecnológico, European Regional Development Fund, Agencia Estatal de Investigación

Awards: Geometry of Banach Spaces, G1422035950, Geometry of Banach spaces, G2262748287, G2327452658, G3480869486, G425668148, G451917667, G5967599077, G6033112984, G6438247056, G7084143925, Interpolation theory and geometry of Banach Spaces, G843564687, G8591315598, G8684520763

OpenAlex ID: W4406022347

Cites:

Cited by:

Related to: 10