2022/04/28 by Antonio Avilés, Stefano Ciaci, Avilés, Antonio +7 · 1 citation
Mathematics · #46B03 #46B04 #46B20 #46B26 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2204.13449
openalex publication_date 2022/04/28 · openalex created_date 2022/05/01 · openalex updated_date 2026/07/28
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].