The Kitai criterion and backward shifts

It is proved that for any separable infinite dimensional Banach space , there is a bounded linear operator on such that satisfies the Kitai criterion. The proof is based on a quasisimilarity argument and on showing that satisfies the Kitai criterion for certain backward weighted shifts .

     

一类拟相似算子的本质谱

引进亚控制算子的概念,通过算子谱的精密结构的分析,给出拟相似亚控制算子的本质谱相等的若干条件,所得结果改进和发展了Williams L R的有关结果.     

算子的拟相似性与本质谱的性质

设算子A和B拟相似,本文通过算子谱的精密结构的分析,给出了算子A的Wolf本质谱、Kato本质谱、Weyl本质谱以及右本质谱的连通分支与算子B的Wolf本质谱的某些子集的相交关系,并肯定地回答了L．A．Fialkow在文献[3]中提出的一个问题．     

RT类算子与右本质谱的连通分支

本文研究两个拟相似算子的右本质谱之间的相交关系.通过引进RT类算子的概念,利用算子谱的精密结构的分析方法,得到一个算子的右本质谱的连通分支与另一个拟相似算子的右本质谱相交的充分和必要条件.     

Spectral structure and subdecomposability of -hyponormal operators

We prove that for every -hyponormal operator there corresponds a hyponormal operator such that and have ``equal spectral structure". We also prove that every -hyponormal operator is subdecomposable. Then some relevant quasisimilarity results are obtained, including that two quasisimilar -hyponormal operators have equal essential spectra.