Weighted Laws of Large Numbers and Weighted One-Sided ergodic Hilbert Transforms on Vector Valued $L_p$-spaces

一致遍历性与单侧遍历希尔伯特变换

Uniform ergodicity and the one-sided ergodic Hilbert transform

本文证明了Banach空间上有界线性算子的一致遍历性等价于单侧遍历Hilbert变换的收敛性，研究了旋转一致遍历性，并指出无穷维空间上的正等距算子绝不一致遍历。

Poisson equation and discrete one-sided Hilbert transform for $(C,α)$-bounded operators

We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for Cesàro bounded operators of fractional order. The results obtained fairly generalize the corresponding ones for power-bounded operators. In passing, we give an extension of the mean ergodic theorem. Examples are given to illustrate the theory.

关于Banach代数中单边Drazin逆的谱恒等式与基本性质

On the spectral identities and fundamental properties of one-sided Drazin inverses in Banach algebras

本文研究了Banach代数中单边（广义）Drazin逆的基本性质，引入单边强pi-正则性并证明其等价于单边Drazin可逆性，进而利用Jacobson引理推导出单边Drazin可逆谱及Fredholm型算子的谱恒等式。

Minimality, homogeneity and topological 0-1 laws for subspaces of a Banach space

If a Banach space is saturated with basic sequences whose linear span embeds into the linear span of any subsequence, then it contains a minimal subspace. It follows that any Banach space is either ergodic or contains a minimal subspace. For a Banach space $X$ with an (unconditional) basis, topological 0-1 law type dichotomies are stated for block-subspaces of $X$ as well as for subspaces of $X$ with a successive FDD on its basis. A uniformity principle for properties of block-sequences, results about block-homogeneity, and a possible method to construct a Banach space with an unconditional ba…

Maximal ergodic inequalities for some positive operators on noncommutative $L_p$-spaces

In this paper, we establish the one-sided maximal ergodic inequalities for a large subclass of positive operators on noncommutative $L_p$-spaces for a fixed $1<p<\infty$, which particularly applies to positive isometries and general positive Lamperti contractions or power bounded doubly Lamperti operators; moreover, it is known that this subclass recovers all positive contractions on the classical Lebesgue spaces $L_p([0,1])$. Our study falls into neither the category of positive contractions considered by Junge-Xu nor the class of power bounded positive invertible operators considered by Hong…