3 papers
math.FA2024
Strictly convex norms and the local diameter two property
Trond A. Abrahamsen, Petr Hájek, Vegard Lima +1
We introduce and study a strict monotonicity property of the norm in solid Banach lattices of real functions that prevents such spaces from having the local diameter two property.…
math.FA2024
Norming Markushevich bases: recent results and open problems
Petr Hájek, Tommaso Russo
We survey several results concerning norming Markushevich bases (M-bases, for short), focusing in particular on two recent examples of a weakly compactly generated Banach space wit…
math.FA2023
Counterexamples in rotundity of norms in Banach spaces
Petr Hájek, Andrés Quilis
We study several classical concepts in the topic of strict convexity of norms in infinite dimensional Banach spaces. Specifically, and in descending order of strength, we deal with…