4 papers
Order closure, order adherence and Fatou norms
A. Avilés, M. A. Taylor, P. Tradacete
We record two results in the theory of vector and Banach lattices related to order adherence. First, we give a negative answer to Gao and Leung's question on whether the -adher…
Transfinite Daugavet property
Antonio Avilés, Johann Langemets, Miguel Martín +1
We extend the Daugavet property and a perfect version of it to transfinite cardinals in order to distinguish between spaces with the ordinary Daugavet property by some kind of comp…
The Dedekind completion of an Archimedean ordered vector space as a reflector
Antonio Avilés, Eugene Bilokopytov
We consider the category of Archimedean ordered vector spaces with linear maps which preserve all existing suprema, and its full subcategories , $\m…
A Classification of Order Convergence via a Transfinite Fatou Hierarchy
Antonio Avilés, Christian Rosendal, Mitchell A. Taylor +1
We investigate the descriptive complexity of order convergence in separable Banach lattices. While uniform convergence is Borel and -order convergence is known to be ${\bf Δ}^1_…