一类闭算子的特征Characteristic of a kind of Closed Operators
杨根科,卫淑芝
摘要(Abstract):
本文引入了闭拟谱算子概念,得到这类闭算子的谱分解特征。推广了Banach空间中纯量型(无界)谱算子以及Well-bounded算子谱分解理论。 主要结果:T为闭拟谱算子的充要条件是T稠定闭,且存在复数u使I_mu≠0以及连续代数同态:Ac_o(R′)—→B(x),使得。
关键词(KeyWords): 单位分解;纯量型谱算子;闭拟谱算子;Well-bounded算子
基金项目(Foundation):
作者(Author): 杨根科,卫淑芝
参考文献(References):
- 1 H.R.Dowson. Spectral Theory of Linear Operators. London Math. soc. Monogrophs, No12.Academic press, New York 1978
- 2 J.R.Ringrose. On Well-bounded Opertors Ⅱ.proc. London.Math.soc. (3) 13.(1963) 613-618
- 3 吉田耕作.泛函分析.人民教育出版社,1981
- 4 H.Benzinger, E.Berkson and T.A.Gillespie. Spectral Families of Pro jections, Semigroup and Differential-Operotors. Trams.Amer.Math.soc. 275(1983)431-475
- 5 E.Berkson. Spectroral familiar of Projections in Hardy Spaces. J.Funct Anal.60 (1985) 146-67
- 6 D.R.Smart.Conditionally Convergert Spectrall expansions, J.Austral Math.Soc. 1 (1960) 319-333