Projections in Lipschitz-free spaces induced by group actions

0575127 - MÚ 2024 RIV DE eng J - Článek v odborném periodiku
Cúth, Marek - Doucha, Michal
Projections in Lipschitz-free spaces induced by group actions.
Mathematische Nachrichten. Roč. 296, č. 8 (2023), s. 3301-3317. ISSN 0025-584X. E-ISSN 1522-2616
Grant CEP: GA ČR(CZ) GJ19-05271Y
Institucionální podpora: RVO:67985840
Klíčová slova: amenable group * group action by isometries * Lipschitz-free space * space of Lipschitz functions
Obor OECD: Pure mathematics
Impakt faktor: 1, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1002/mana.202100222

We show that given a compact group G acting continuously on a metric space (Figure presented.) by bi-Lipschitz bijections with uniformly bounded norms, the Lipschitz-free space over the space of orbits (Figure presented.) (endowed with Hausdorff distance) is complemented in the Lipschitz-free space over (Figure presented.). We also investigate the more general case when G is amenable, locally compact or SIN and its action has bounded orbits. Then, we get that the space of Lipschitz functions (Figure presented.) is complemented in (Figure presented.). Moreover, if the Lipschitz-free space over (Figure presented.), (Figure presented.), is complemented in its bidual, several sufficient conditions on when (Figure presented.) is complemented in (Figure presented.) are given. Some applications are discussed. The paper contains preliminaries on projections induced by actions of amenable groups on general Banach spaces.
Trvalý link: https://hdl.handle.net/11104/0344982