非游荡算子的性质

本文研究一类具有混纯性质的线性算子：非游荡算子，该类算子仅在无穷维线性空间中．我们给出非游荡算子紧集上的超循环分解．     

Nilpotent operators similar to irreducible operators

We give a necessary and sufficient condition for the nilpotent operators to be similiar to irreducible operators, and give an answer to D. A. Herrero Conjectures for nilpotent operators.     

Disjointly homogeneous Banach lattices and compact products of operators

The notion of disjointly homogeneous Banach lattice is introduced. In these spaces every two disjoint sequences share equivalent subsequences. It is proved that on this class of Banach lattices the product of a regular AM-compact and a regular disjointly strictly singular operators is always a compact operator.     

广义弱亚正规算子的正规性

主要研究了T是广义弱亚正规算子时,T~t是拟正规算子的充要条件是T是拟正规算子.并且举例说明了存在非次正规的广义弱亚正规算子T使得T~t是次正规的.     

冯·诺依曼代数的可测算子的性质

本文研究了冯·诺依曼代数的可测算子的基本性质,定义了阶梯算子,证明了任意一个正可测算子可以由阶梯算子在定义域内按照强算子拓扑逼近,从而证明了任意一个可测算子可以由投影在定义域内按照强算子拓扑逼近.此外,还讨论了可测算子与有界算子的复合算子的可测性.     

Oscillation and variation for Riesz transform in setting of Bessel operators on H1 and BMO

Let \lambda >\mathrm{0} and let the Bessel operator \mathrm{\Delta }\lambda ：=-{\displaystyle \frac{{\mathrm{d}}^{\mathrm{2}}}{{\mathrm{d}x}^{\mathrm{2}}}}-{\displaystyle \frac{\mathrm{2}\lambda }{x}}{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}} defined on {{\displaystyle ℝ}}_{+}:=(\mathrm{0},\infty ). We show that the oscillation and \rho-variation operators of the Riesz transform {{\displaystyle R}}_{{\mathrm{\Delta }}_{\lambda }} associated with {\mathrm{\Delta }}_{\lambda } are bounded on BMO({{\displaystyle ℝ}}_{+},{{\displaystyle dm}}_{\lambda }), where \rho >\mathrm{2} and {{\displaystyle \mathrm{d}m}}_{\lambda }=x^{\mathrm{2}\lambda }\mathrm{d}x. Moreover, we construct a {{\displaystyle (\mathrm{1},\infty )}}_{{\mathrm{\Delta }}_{\lambda }}-atom as a counterexample to show that the oscillation and \rho-variation operators of {{\displaystyle R}}_{{\mathrm{\Delta }}_{\lambda }} are not bounded from H^{\mathrm{1}}({ℝ}^{+},{{\displaystyle \mathrm{d}m}}_{\lambda }) to L^{\mathrm{1}}({ℝ}^{+},{{\displaystyle \mathrm{d}m}}_{\lambda }). Finally, we prove that the oscillation and the {{\displaystyle (\mathrm{1},\infty )}}_{{\mathrm{\Delta }}_{\lambda }}-variation operators for the smooth truncations associated with Bessel operators {{\displaystyle \tilde{R}}}_{{\mathrm{\Delta }}_{\lambda }} are bounded from H^{\mathrm{1}}({ℝ}^{+},{{\displaystyle \mathrm{d}m}}_{\lambda }) to L^{\mathrm{1}}({ℝ}^{+},{{\displaystyle \mathrm{d}m}}_{\lambda }).     

模糊算子排序

完成了几种常用的模糊算子的排序工作.     

解析函数的Banach空间上之复合算子

本文研究了一类解析函数的Ｂａｎａｃｈ空间Ｘ上之复合算子，这类空间包含了Ｂｌｏｃｈ空间，并且可看作Ｂｅｒｇｍａｎ空间Ｌ１ａ（Ｄ）中具有原子分解的解析函数的对偶空间．我们刻划了这类空间上紧复合算子及Ｆｒｅｄｈｏｌｍ复合算子的特征，此外，还研究了具有闭值域的复合算子．     

M/Mk,B/1算子的豫解集

首先运用Phillips定理和Fattorini定理证明M／M^k，^B／1排队模型概率瞬态解的存在唯一性，然后通过研究对应于M／M^k，^B／1排队模型的主算子的共轭算子的豫解集得到该主算子的豫解集：在虚轴上除了零点外其它所有点都属于该主算子的豫解集．