Counterexample to the Trotter product formula for projections

A counterexample to a conjecture of Akemann and Anderson

Akemann and Anderson made a conjecture about ``paving'' projections in finite dimensional matrix algebras which, if true, would settle the well-known Kadison-Singer problem. We falsify their conjecture by an explicit seqence of counterexamples.

On quasi-contractivity of $C_0$-semigroups on Banach spaces

A basic result in semigroup theory states that every $C_0$-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula $(e^{\frac{t}{n}A}P)^n$ (where $P$ denotes a bounded projection), we prove that whenever the generator $A$ is unbounded it is possible to introduce an equivalent norm on the space with respect to which the semigroup is {\it{not}} quasi-contractive.

Hilbert与Banach空间中算子变换与谱投影的超限迭代

Transfinite Iteration of Operator Transforms and Spectral Projections in Hilbert and Banach Spaces

研究了有界算子变换多层迭代的收敛性，在泛函演算假设下证明了向谱投影的强收敛，并提供了显式滤波器、单调性界及反例。

关于松弛投影无穷乘积的有界性：扰动弹性与动态字符串平均

On the boundedness of infinite products of relaxed projections: perturbations resilience and dynamic string-averaging

本研究在鲍施克和董的基础上，通过允许扰动、考虑闭半空间与超平面混合及使用动态加权和等方式扩展其关于松弛投影无穷乘积有界性的结果，还讨论推广局限并建立赋范空间压缩映射无穷乘积相关定理。

逆生成元问题及相关问题的一个反例

A solution to the inverse generator problem and related questions

该研究在希尔伯特空间上构造反例，否定了逆生成元问题，证明了克兰克-尼科尔森格式在算子范数下的不稳定性，反例源于有限维构造及绍德尔乘子方法。