论文标题
关于无条件基础正方形的排列性等效性
On the permutative equivalence of squares of unconditional bases
论文作者
论文摘要
我们证明，如果两个无条件基础的平方等于置换，则基础本身是定制的。这解决了卡萨扎（Casazza）和卡尔顿（Kalton）提出的一个二十岁的问题[以色列J. Math的Banach空间中的无条件基地的独特性。 103（1998），141--175]。解决此问题提供了一个新的范式，以研究准巴纳奇空间一般框架中无条件基础的独特性。给出了多个示例，以说明如何实践该理论方案。在该原则的主要应用中，我们获得了无条件基础的唯一性，直到使用该特性的准雪橇空间有限总和的排列。
We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty year-old question raised by Casazza and Kalton in [Uniqueness of unconditional bases in Banach spaces, Israel J. Math. 103 (1998), 141--175]. Solving this problem provides a new paradigm to study the uniqueness of unconditional basis in the general framework of quasi-Banach spaces. Multiple examples are given to illustrate how to put in practice this theoretical scheme. Among the main applications of this principle we obtain the uniqueness of unconditional basis up to permutation of finite sums of quasi-Banach spaces with this property.
