论文标题
连接几乎是正方形的Banach空间
Transfinite almost square Banach spaces
论文作者
论文摘要
众所周知，Banach空间包含$ C_0 $的同构副本，并且只有当它等效地将其等同于几乎是正方形的情况下。我们介绍并研究了几乎方形的Banach空间的传播版本，其目的是将它们与$ C_0（κ）$的同构副本的遏制有关，其中$κ$是一种无法数量的基数。我们还通过采用直接总和，张量产品和超强功能来提供上述特性的几个示例和稳定性结果。通过将上述特性与强直径的两个特性和八面体规范的转线类似物联系起来，我们从[8]中获得了一个解决方案的解决方案。
It is known that a Banach space contains an isomorphic copy of $c_0$ 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 $c_0(κ)$, 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].
