Nonatomic submeasures on $\mathbb N$ and the Banach space $\ell_1$

关于非原子巴拿赫格和Hardy空间

On nonatomic Banach lattices and Hardy spaces

我们感兴趣的问题是，当一个巴拿赫空间$X$与一个无条件基同构（作为一个巴拿赫空间）的顺序连续的非原子巴拿赫格。我们证明了这是当且仅当$X$是同构的巴拿赫空间与$X(\ell_2)$。这和J. Bourgain的结果被用来证明空间$H_1(\bold T^n)$不同构于非原子巴拿赫格。我们还证明了在\cite{4}中引入的帐篷空间同构于Rad $H_1$ .

集函数与因子分解

Set-functions and factorization

若$ϕ$是满足适当下估计的子测度，则给出了满足$0\leμ\leϕ.$的测度$ϕ$的总质量的一个定量结果，给出了超测度的对偶结果，并利用这些结果研究了非局部凸拟巴拿赫格上的凸性。然后，我们展示了如何使用这些结果，以延长一些因式分解定理，由于皮西尔设置准巴拿赫空间。证明了若$X$是拟Banach空间的余型2，则任何算子$T:C(Ω)\to X$都是2-绝对和的，且因子通过希尔伯特空间，并讨论了余型2空间的一般因子分解定理.

Analytic P-ideals and Banach spaces

We study the interplay between Banach space theory and theory of analytic P-ideals. Applying the observation that, up to isomorphism, all Banach spaces with unconditional bases can be constructed in a way very similar to the construction of analytic P-ideals from submeasures, we point out numerous symmetries between the two theories. Also, we investigate a special case, the interactions between combinatorics of families of finite sets, topological properties of the "Schreier type" Banach spaces associated to these families, and the complexity of ideals generated by the canonical bases in these…

格罗滕迪克空间与强正规序列的自反性

Reflexivity of Grothendieck Spaces and Strongly Normal Sequences

该研究刻画了格罗滕迪克空间自反性与正规序列子序列行为的等价关系，给出正规序列含强正规子序列的商准则，并构造了相关实例。

A simple Efimov space with sequentially-nice space of probability measures

Under Jensen's diamond principle $\diamondsuit$, we construct a simple Efimov space $K$ whose space of nonatomic probability measures $P_{na}(K)$ is first-countable and sequentially compact. These two properties of $P_{na}(K)$ imply that the space of probability measures $P(K)$ on $K$ is selectively sequentially pseudocompact and the Banach space $C(K)$ of continuous functions on $K$ has the Gelfand-Phillips property. We show also that any sequence of probability measures on $K$ that converges to an atomic measure converges in norm, and any sequence of probability measures on $K$ converging to…