Lu CuiAcademy of Mathematics and Systems Science, Chinese Academy of SciencesLinzhe HuangTsinghua University, YMSCWenming WuSchool of Mathematical Sciences, Chongqing Normal UniversityWei YuanAcademy of Mathematics and Systems Science, Chinese Academy of SciencesHanbin ZhangSchool of Mathematics (Zhuhai), Sun Yat-sen University
Journal of Mathematical Analysis and Applications, 21, 2022.4
A unital ring is called clean (resp. strongly clean) if every element can be written
as the sum of an invertible element and an idempotent (resp. an invertible element
and an idempotent that commutes). T.Y. Lam proposed a question: which von
Neumann algebras are clean as rings? In this paper, we characterize strongly clean
von Neumann algebras and prove that all finite von Neumann algebras and all
separable infinite factors are clean.
Johannes SjöstrandInstitut de Mathématiques de Bourgogne, Université de Bourgogne Franche-Comté, Dijon, FranceMaher ZerzeriLaboratoire Analyse, Géométrie et Applications, Université Sorbonne Paris-Nord, Villetaneuse, France
Analysis of PDEsFunctional Analysismathscidoc:2203.03008
In this paper we study the distribution of scattering resonances for a multi-dimensional semi-classical Schrödinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.
We prove that log n is an almost everywhere convergence Weyl multiplier for the orthonormal systems of non-overlapping Haar polynomials. Moreover, it is done for the general systems of martingale difference polynomials.