Banach空间中单侧加权移位的谱性质和拟相似Spectral Properties of Unilateral Weighted Shifts and Quasisimilarity in Banach Space
严子锟;
摘要(Abstract)：
本文给出了Banach空间中单侧加权移位的谱性质,证明了当对应的基是无条件基时,两个单侧加权移位的拟相似性、稠值域相似性、相似性是等价的,推广并加强了已有的有关结果。
关键词(KeyWords)： Banach空间;单侧加权移位;拟相似;谱
基金项目(Foundation):
作者(Authors): 严子锟;
参考文献(References)：
- [1] Lambert A. Strictly Cyclic Operator Algebras. Ph. D. Thesis, University of Michigan, 1970．
- [2] 俞鑫泰.Banach空间几何理论.上海:华东师范大学出版社,1986．
- [3] Shields A L. Weighted shift operators analytic function theory. Topics in Operator Theory Amer. Math. Soc. Providence, 1974, 13 : 49～128
- [4] Herrero D A. The Fredholm structure of an n-multicyclic operator. Indiana U. Math. J., 1987, 36 : 549～566
- [5] Ralph Gellar. Operators commuting with a weighted shift. Proc. Amer. Soc., 1969． 23 : 538～545
- [6] 林辰,严子锟.次正常算子的拟相似算子本质谱.科学通报,1992,37(8) :685～688
- [7] Lindenstrauss J, Zippin M. Bausch spaces with a unique unconditional basis. J. Functional Analysis, 1969, 3(1) : 115～125
- [8] Lindenstrauss J, Tzafriri L. Classical Banach Spaces Ⅰ. Berlin Heidelberg NeW York: Springee-Verlag, 1977