6 papers
Lipschitz-free spaces over separable Banach spaces and their complementability in the bidual
Marek Cúth, Ondřej F. K. Kalenda
We prove that the Lipschitz-free space over a separable Banach space is complemented in its bidual if and only if the underlying Banach space is isomorphic to a Hilbert space. This…
Isometries without linear shadows: failure of Figiel's theorem beyond local convexity
Fernando Albiac, José L. Ansorena, Marek Cúth
A classical theorem of Figiel asserts that every isometric embedding between real Banach spaces, with , admits a linear contractive left inverse on the clo…
Structural consequences of the Schur -property for Lipschitz-free -spaces
Fernando Albiac, José L. Ansorena, Marek Cúth
Let . We show that the Schur -property provides a powerful structural principle for Lipschitz-free -spaces. Our main result asserts that has t…
Lipschitz-free spaces over uniformly discrete metric spaces are 3-Schur
Marek Cúth, Ondřej F. K. Kalenda
We prove that the Lipschitz-free space over any uniformly discrete metric space has the 3-Schur property
The classification of spaces for countable compacta by positive isomorphisms
Marek Cúth, Jonáš Havelka, Jakub Rondoš +1
We study the classification of spaces of continuous functions under positive linear maps. For infinite countable compacta, we show that whenever and are isomor…
Lipschitz free -spaces for in the light of the Schur -property and the compact reduction
Fernando Albiac, José L. Ansorena, Jan Bíma +1
The geometric analysis of non-locally convex quasi-Banach spaces presents rich and nuanced challenges. In this paper, we introduce the Schur -property and the strong Schur -p…