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Transfinite octahedrality in spaces of operators
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.
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BibTeX
@misc{zoca2026transfinite,
title = {{Transfinite octahedrality in spaces of operators}},
author = {Abraham Rueda Zoca},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24414},
eprint = {2609.24414},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24414},
}
RIS
TY - UNPB
TI - Transfinite octahedrality in spaces of operators
AU - Abraham Rueda Zoca
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24414
UR - https://arxiv.org/abs/2609.24414
AB - 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.
ER -