非游荡算子半群标准及应用

根据非游荡算子半群的定义得到了非游荡算子半群的几个性质,给出了判定算子半群是非游荡半群的标准,应用给出的标准,在空间C([0,1],C)上讨论了偏微分方程au/at=γx(au/ax)+h(x)u,u(0,x)=f(x)的解半群的性质.     

The abelianization of hypercyclic groups

Let G be a hypercyclic group. The most substantial results of this paper are the following. a) If G/G′ is 2-divisible, then G is 2-divisible. b) If G/G′ is a 2′-group, then G is a 2′-group. c) If G/G′ is divisible by finite-of-odd-order, then G/V is divisible by finite-of-odd-order, where V is the intersection of the lower central series (continued transfinitely) of O _2′ (G).      

On the existence of chaotic and hypercyclic semigroups on Banach spaces

We prove that every separable infinite dimensional complex Banach space admits a hypercyclic uniformly continuous semigroup. We also prove that there exist Banach spaces admitting no chaotic strongly continuous semigroups.

     

算子矩阵的亚循环性

讨论了亚循环算子和具有拓扑一致降标的算子之间的关系,同时研究了算子矩阵的亚循环性和超循环性.     

The range of operators on von Neumann algebras

We prove that for every bounded linear operator , where is a non-reflexive quotient of a von Neumann algebra, the point spectrum of is non-empty (i.e., for some the operator fails to have dense range). In particular, and as an application, we obtain that such a space cannot support a topologically transitive operator.

     

Porosity and hypercyclic operators

We study if the set of hypercyclic vectors of a hypercyclic operator is the complement of a -porous set. This leads to interesting results for both points of view: a limitation of the size of hypercyclic vectors, and new examples of first category sets which are not -porous.

     

Complete systems of partial derivatives of entire functions and frequently hypercyclic operators

We find some sufficient conditions for a system of partial derivatives of an entire function to be complete in the space H(C^d)$H({\mathbb{C}}^d)$ of all entire functions of d   variables. As an application of this result we describe new classes of frequently hypercyclic operators on H(C^d)$H({\mathbb{C}}^d)$.     

A remark on the Frequent Hypercyclicity Criterion for weighted composition semigroups and an application to the linear von Foerster–Lasota equation

We generalize a result for the translation C₀‐semigroup on about the equivalence of being chaotic and satisfying the Frequent Hypercyclicity Criterion due to Mangino and Peris 8 to certain weighted composition C₀‐semigroups. Such C₀‐semigroups appear in a natural way when dealing with initial value problems for linear first order partial differential operators. We apply our result to the linear von Foerster–Lasota equation arising in mathematical biology. Weighted composition C₀‐semigroups on Sobolev spaces are also considered.