Journal of East China Normal University(Natural Science) ›› 2020, Vol. 2020 ›› Issue (2): 1-7.doi: 10.3969/j.issn.1000-5641.201911004

• Mathematics •     Next Articles

Property of the consistent Fredholm index and property (ω1)

DAI Lei   

  1. School of Mathematics and Statistics, Weinan Normal University, Weinan Shaanxi 714099, China
  • Received:2019-01-06 Published:2020-03-16

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

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