重单值扩张算子的谱结构与拟相似

本文证明了,若T是重单值扩张算子,则若T1是重单值扩张（C）算子,T2是任一有界线性算子,T1与T2拟相似,则σe（T1）＝σk（T1）σk（T2）＝σe（T2）     

算子的左本质谱与Browder本质谱

设算子S和T拟相似,应用算子谱的精密结构的分析,证明了Browder本质谱σB(S)的连通分支与σB(T)的某些子集的相交关系以及左本质谱σle(S)的连通分支与本质谱σe(T)的某些子集的相交关系,给出左本质谱σle(S)的连通分支与σle(T)相交的充分条件和充要条件.     

Bishop's property () and essential spectra of quasisimilar operators

We analyze the notion of Bishop's property () to obtain some new concepts. We describe some conditions in terms of these concepts for an operator to have its essential spectrum (spectrum) contained in the essential spectrum (spectrum) of every operator quasisimilar to it. A subfamily of such operators is proved to be dense in .

     

Quasisimilarity of power bounded operators and Blum-Hanson property

We construct a power bounded operator on a Hilbert space which is not quasisimilar to a contraction. To this aim, we solve an open problem from operator ergodic theory showing that there are power bounded Hilbert space operators without the Blum-Hanson property. We also find an example of a power bounded operator quasisimilar to a unitary operator which is not similar to a contraction, thus answering negatively open questions raised by Kérchy and Cassier. On the positive side, we prove that contractions on ?p spaces (1?p<∞) possess the Blum-Hanson property.     

拟相似算子的右本质谱的连通分支

设算子S和T拟相似,通过引进RT类算子、R类算子和RR类算子的概念,给出右本质谱σre(S)的连通分支与σre(T)相交的充分条件和必要条件以及σre(S)的连通分支与本质谱盯σe(T)的某些子集的相交关系,并给出算子是属于RT类算子和RR类算子的充分条件和必要条件.     

Confluent operator algebras and the closability property

Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the transitive algebra problem. More precisely, if A is a two-transitive algebra with the closability property, then A is dense in the algebra of all bounded operators, in the weak operator topology. In this paper we focus on algebras generated by a completely nonunitary contraction, and produce several new classes of algebras with the closability property. We show that this property follows from a certain strict cyclicity property, and we give very detailed information on the class of completely nonunitary contractions satisfying this property, as well as a stronger property which we call confluence.     

p-亚正常算子的本质谱与拟相似

本文证明了每一个ｐ－亚正常算子Ａ,都相应存在一个亚正常算子 ,使得Ａ与 有相同的闭值域点、相同的本质谱和谱．由此推出如果Ａ是ｐ－亚正常算子,Ｂ是任一有界线性算子,若存在有界线性算子Ｘ有稠值域,使得ＸＢ＝ＡＸ,则σ（Ａ）（Ｂ）此外还证明了,如果Ａ是ｐ－亚正常算子且 Ｒ（Ａ）闭或ＫｅｒＡ＝ＫｅｒＡ*, Ｂ是任一有界线性算子,Ａ与Ｂ拟相似,则ｅ（Ａ）（Ｂ）．     

算子的拟相似与(Q)类算子

本文引进定义于L(H)上的集值函数β(S)和(Q)类算子(指本质谱含于其一切拟相似算子的本质谱的算子),用β(S)刻划 (Q)类算子的特征;证明(Q)类算子范围广泛,次可分解算子(包括次标量算子,M-亚正常算子,半亚正常算子等等)是其中的一部分;(Q)类算子在L(H)中稠密.