论文标题
$ \ ell_ {2} \ oplus \ mathcal {t}^{（2）} $的无条件基础的唯一性
Uniqueness of unconditional basis of $\ell_{2}\oplus \mathcal{T}^{(2)}$
论文作者
论文摘要
我们提供了Pitt的定理的新扩展，用于在准巴纳赫晶格之间进行紧凑型操作员，该定理允许描述Banach Space $ \ Mathbb {X} _ {1} \ oplus \ dots \ oplus \ oplus \ oplus \ poplus \ oplus \ mathbb {x} $ sund的无条件直接总和的无条件基础。我们获得的一般拆分原则特别是，如果每个$ \ mathbb {x} _ {i} $具有唯一的无条件基础（直至等价和置换），则$ \ mathbb {x} _ {1} \ oplus \ oplus \ cdots \ cdots \ cdots \ oplus \ oplus \ oplus \ poplus \ oplus \ mathbb =在我们技术对Banach和Quasi-Banach空间结构的新颖应用中，我们有空间$ \ ell_2 \ oplus \ Mathcal \ Mathcal {t}^{（2）} $具有独特的无条件基础。
We provide a new extension of Pitt's theorem for compact operators between quasi-Banach lattices, which permits to describe unconditional bases of finite direct sums of Banach spaces $\mathbb{X}_{1}\oplus\dots\oplus\mathbb{X}_{n}$ as direct sums of unconditional bases of its summands. The general splitting principle we obtain yields, in particular, that if each $\mathbb{X}_{i}$ has a unique unconditional basis (up to equivalence and permutation), then $\mathbb{X}_{1}\oplus \cdots\oplus\mathbb{X}_{n}$ has a unique unconditional basis too. Among the novel applications of our techniques to the structure of Banach and quasi-Banach spaces we have that the space $\ell_2\oplus \mathcal{T}^{(2)}$ has a unique unconditional basis.
