Transfinite almost square Banach spaces Avilés, Antonio Rueda Zoca, Abraham c0(κ) Almost square space Octahedral norm Renorming 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]. 2023-03-10T12:41:08Z 2023-03-10T12:41:08Z 2022-04-28 journal article Published version: Avilés, A... [et al.]. Transfinite almost square Banach spaces. Studia Mathematica, 1-25. DOI: [10.4064/sm220517-4-11] https://hdl.handle.net/10481/80530 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Polish Academy of Sciences