Property of the consistent Fredholm index and property (ω<sub>1</sub>)

DAI Lei

doi:10.3969/j.issn.1000-5641.201911004

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

Citation:

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

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

Citation:

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

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Property of the consistent Fredholm index and property (ω₁)

doi: 10.3969/j.issn.1000-5641.201911004

DAI Lei

School of Mathematics and Statistics, Weinan Normal University, Weinan Shaanxi　714099, China

Received Date: 2019-01-06
Publish Date: 2020-03-01

Abstract

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 $(\omega_1)$. In addition, the paper explores the relationship between the property $(\omega_1)$ and hypercyclic operators (or supercyclic operators). Meanwhile, new conditions for hypercyclic operators and supercyclic operators are given.
- property $(\omega_1)$,
- hypercyclic operator,
- property of the consistent Fredholm index,
- spectrum

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References(11)

References

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