Journal of East China Normal University(Natural Science) >

2020 , Vol. 2020 >Issue 2: 1 - 7

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911004

Mathematics

Property of the consistent Fredholm index and property (ω1)

  • DAI Lei
Expand
  • School of Mathematics and Statistics, Weinan Normal University, Weinan Shaanxi　714099, China

Received date: 2019-01-06

  Online published: 2020-03-16

Fold

Abstract

In this paper, a new spectrum is defined according to the property of the consistent Fredholm index. We establish the sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space that satisfies the property (ω1). In addition, the paper explores the relationship between the property (ω1) and hypercyclic operators (or supercyclic operators). Meanwhile, new conditions for hypercyclic operators and supercyclic operators are given.

Key words： property (ω1); hypercyclic operator; property of the consistent Fredholm index; spectrum

Cite this article

DAI Lei . Property of the consistent Fredholm index and property (ω1)[J]. Journal of East China Normal University(Natural Science), 2020 , 2020(2) : 1 -7 . DOI: 10.3969/j.issn.1000-5641.201911004

References

[1] WEYL H. Über beschränkte quadratische formen, deren differenz vollstetig ist[J]. Rendiconti Del Circolo Matematico Di Palermo, 1909, 27(1):373-392. DOI:10.1007/BF03019655.
[2] RAKOČEVIĆ V. On a class of operators[J]. Matematicki Vesnik, 1985, 37(4):423-426.
[3] RAKOČEVIĆ V. Operators obeying a-Weyl's theorem[J]. Romanian Journal of Pure and Applied Mathematics, 1989, 34(10):915-919.
[4] BERKANI M, KOLIHA J J. Weyl type theorems for bounded linear operators[J]. Acta Scientiarum Mathematicarum, 2003, 69(1/2):359-376.
[5] SUN C H, CAO X H, DAI L. Property (ω1) and Weyl type theorem[J]. Journal of Mathematical Analysis and Applications, 2010, 363(1):1-6. DOI:10.1016/j.jmaa.2009.07.045.
[6] CAO X H. Weyl spectrum of the products of operators[J]. Journal of the Korean Mathematics Society, 2008, 45:771-780. DOI:10.4134/JKMS.2008.45.3.771.
[7] 曹小红, 刘俊英. 一致Fredholm及广义(ω')指标算子性质[J]. 数学学报, 2010, 53(5):953-962
[8] 戴磊, 曹小红, 张建华, 等. CFI算子和Weyl型定理[J]. 数学进展, 2014, 43(4):590-598. DOI:10.11845/sxjz.2012159b
[9] CONWAY J. A Course in Functional Analysis[M]. New York:Springer-Verlag, 1990.
[10] KITAI C. Invariant closed sets for linear operators[D]. Toronto:University of Toronto, 1982.
[11] HERRERO D A. Limits of hypercyclic and supercyclic operators[J]. Journal of Functional Analysis, 1991, 99(1):179-190. DOI:10.1016/0022-1236(91)90058-D.
Options
Outlines

/

〈 〉