A counterexample to a conjecture of S.E. Morris

Counterexamples to the discrete and continuous weighted Weiss conjectures

Counterexamples are presented to weighted forms of the Weiss conjecture in discrete and continuous time. In particular, for certain ranges of $α$, operators are constructed that satisfy a given resolvent estimate, but fail to be $α$-admissible. For $α\in (-1,0)$ the operators constructed are normal, while for $α\in (0,1)$ the operator is the unilateral shift on the Hardy space $H^2(\mathbb{D})$.

Another counterexample to Zygmund's conjecture

We present a simple dyadic construction that yields a new counterexample to Zygmund's conjecture. Our result recovers Soria's classical result in dimension three, through a different construction, and gives new ones in all other dimensions $d > 3$.

Arveson超刚性猜想的一个有限维反例

A Finite Dimensional Counterexample for Arveson's Hyperrigidity Conjecture

该研究构造了由4个算子生成的算子系统作为反例，证明即使不可约表示的所有限制都有唯一扩张性质，该系统仍不满足超刚性，为Arveson超刚性猜想提供了有限维反证。

A Counterexample to a Conjecture of Gomory and Johnson

In Mathematical Programming 2003, Gomory and Johnson conjecture that the facets of the infinite group problem are always generated by piecewise linear functions. In this paper we give an example showing that the Gomory-Johnson conjecture is false.

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.

A counterexample to Khabibullin's conjecture for integral inequalities

Khabibullin's conjecture for integral inequalities has two numeric parameters $n$ and $α$ in its statement, $n$ being a positive integer and $α$ being a positive real number. This conjecture is already proved in the case where $n>0$ and $0<α\leq 1/2$. However, for $α>1/2$ it is not always valid. In this paper a counterexample is constructed for $n=2$ and $α=2$. Then Khabibullin's conjecture is reformulated in a way suitable for all $α>0$.