Kreps-Yan theorem for Banach ideal spaces

The Kreps-Yan theorem for $L^\infty$

We prove the following version of the Kreps-Yan theorem. For any norm closed convex cone $C\subset L^\infty$ such that $C\cap L_+^\infty=\{0\}$ and $C\supset -L_+^\infty$, there exists a strictly positive continuous linear functional, whose restriction on $C$ is non-positive. The proof uses some tools from convex analysis in contrast to the case of a weakly Lindelöf Banach space, where such approach is not needed.

关于Banach空间中拟幂零算子的幂集

On the Power Set of Quasinilpotent Operators in Banach Spaces

本文证明Banach空间上每个拟幂零算子T的幂集Λ(T)必含1，并引入均匀重无穷概念，构造出幂集为任意右闭含1子集的算子。

复域上的巴拿赫等距猜想

Banach's Isometric Conjecture over the Complex Field

该研究完成复域巴拿赫等距猜想证明，还证四元数域对应结论，用Lu和Yang的丛次数机制完成核心几何论证，且将结果推广到多类空间与度量。

Conditional quasi-greedy bases in non-superreflexive Banach spaces

For a conditional quasi-greedy basis $\mathcal{B}$ in a Banach space the associated conditionality constants $k_{m}[\mathcal{B}]$ verify the estimate $k_{m}[\mathcal{B}]=\mathcal{O}(\log m)$. Answering a question raised by Temlyakov, Yang, and Ye, several authors have studied whether this bound can be improved when we consider quasi-greedy bases in some special class of spaces. It is known that every quasi-greedy basis in a superreflexive Banach space verifies $k_{m}[\mathcal{B}]=(\log m)^{1-ε}$ for some $0<ε<1$, and this is optimal. Our first goal in this paper will be to fill the gap in betw…

拟幂零后向加权移位的幂集

The power set of a quasinilpotent backward weighted shift

研究巴拿赫空间上拟幂零算子的幂集，证明对任意巴拿赫空间上的拟幂零算子\(1\in\Lambda(T)\)，还表明\(\ell^p\)上特定后向单侧加权移位的\(\Lambda(T)=[0,1]\)，回答了相关问题并弱化了前人假设。

复Banach等距猜想

The Complex Banach Isometric Conjecture

本文证明复Banach等距猜想：若赋范空间所有固定维数（大于1）子空间线性等距，则必为Hilbert空间，通过丛-度方法刻画复超平面截口为Hermite椭球。