@misc{10481/80530,
year = {2022},
month = {4},
url = {https://hdl.handle.net/10481/80530},
abstract = {It is known that a Banach space contains an isomorphic
copy of c0 if, and only if, it can be equivalently renormed to be almost
square. We introduce and study transfinite versions of almost square
Banach spaces with the purpose to relate them to the containment of
isomorphic copies of c0(κ), where κ is some uncountable cardinal. We
also provide several examples and stability results of the above properties
by taking direct sums, tensor products and ultraproducts. By
connecting the above properties with transfinite analogues of the strong
diameter two property and octahedral norms, we obtain a solution to
an open question from [8].},
organization = {MTM2017-
86182-P (funded by MCIN/AEI/10.13039/501100011033 and “ERDF A way
of making Europe”)},
organization = {Fundación Séneca [20797/PI/18]},
organization = {Estonian Research Council grants (PSG487) and (PRG1901)},
organization = {MCIN/AEI/10.13039/
501100011033 (Spain) Grant PGC2018-093794-B-I00},
organization = {Junta de Andalucía
Grant A-FQM-484-UGR18},
organization = {Junta de Andaluc´ıa Grant FQM-0185},
publisher = {Polish Academy of Sciences},
keywords = {c0(κ)},
keywords = {Almost square space},
keywords = {Octahedral norm},
keywords = {Renorming},
title = {Transfinite almost square Banach spaces},
author = {Avilés, Antonio and Rueda Zoca, Abraham},
}