β-operator in Banach Spaces

FAN Li-ying; ZHANG Jia-ning; CAO Li-ping; SONG Jing-jing

doi:10.15938/j.jhust.2018.02.025

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β-operator in Banach Spaces

更新时间：2026-08-31

- β-operator in Banach Spaces
- Vol. 23, Issue 2, Pages: 140-143(2018)
- 作者机构：
  
  哈尔滨理工大学应用数学系,黑龙江,哈尔滨,150080
- 作者简介：
- 基金信息：
- DOI：10.15938/j.jhust.2018.02.025
  CLC： O177.7
- Published：2018
- 稿件说明：
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FAN Li-ying, ZHANG Jia-ning, CAO Li-ping, et al. β-operator in Banach Spaces[J]. 2018, 23(2): 140-143.
DOI：

FAN Li-ying, ZHANG Jia-ning, CAO Li-ping, et al. β-operator in Banach Spaces[J]. 2018, 23(2): 140-143. DOI： 10.15938/j.jhust.2018.02.025.

摘要

:为了研究 Banach 空间算子的一些几何性质，给出了 β 算子和弱 β 算子的定义; 讨论了 β 算子和弱 β 算子的性质，进一步得到了算子具有 β 性质的充分必要条件、 β 算子与具有 β 性质的空间之间的关系，研究了 β 算子空间的定义及此空间的性质，得到了 β 算子是紧算子的判别条件，给出了自反空间一个新的特征。

Abstract

To study some geometric properties of Banach space operator，the definitions of the β-operator and weak β-operator were given，and the properties of the β-operator and weak β-operator were discussed. Sufficient and necessary conditions for the operator with β-property were obtained. The relationship between properties of βoperator and the space which has β-property were discussed. The definition of β-operator space and the property of this space were studied. The conclusion was obtained that β-operator is a compact operator，and a new feature of reflexive space was given.

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Related Institution

School of Material Science and Engineering，Harbin University of Science and Technology

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School of Material Science and Engineering, Harbin University of Science and Technology

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