Year: 2026
Type: preprint
Abstract: We study necessary and sufficient conditions on a Banach space $X$ such that $L(Y,X)$ is transfinite (rigid) octahedral for any Banach space $Y$. We present several examples of such $X$. As application of our results, we find the first example in the literature of Banach space which is rigid octahedral but fails any transfinite version of octahedrality. We also improve some previous results about octahedrality in ultrapower spaces.
Source: arXiv (Cornell University)
Author: Zoca, Abraham Rueda
Institution: Universidad de Granada
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214047451