Hilbert空间中的算子非紧性测度

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 1003-1008.

Hilbert空间中的算子非紧性测度

沈钦锐^*(),孙俊俊()

闽南师范大学数学与统计学院福建漳州363000

收稿日期:2022-06-09 修回日期:2023-02-13 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 沈钦锐 E-mail:qinrui327@163.com;2668318714@qq.com
作者简介:孙俊俊，E-mail: 2668318714@qq.com
基金资助:
国家自然科学基金(11801255);福建省自然科学基金面上项目(2020J01798)

Measure of Non-Compactness of Operators in Hilbert Space

Shen Qinrui^*(),Sun Junjun()

School of Mathematics and Statistics, Minnan Normal University, Fujian Zhangzhou 363000

Received:2022-06-09 Revised:2023-02-13 Online:2023-08-26 Published:2023-07-03
Contact: Qinrui Shen E-mail:qinrui327@163.com;2668318714@qq.com
Supported by:
NSFC(11801255);NSF of FuJian Province(2020J01798)

摘要/Abstract

摘要：

该文利用经典的Hausdorff非紧性测度理论研究了Banach空间中(特殊地, Hilbert 空间中)的算子非紧性测度. 具体地, 先给出Banach空间中算子非紧性测度的表示问题, 及其在全空间与子空间上的限制测度的等价问题; 最后研究了Hilbert 空间之间的有界算子序列的几个半范数相互等价的关系性质, 特别地, 其中包括了一种由Hausdorff测度生成的算子半范数.

关键词: 非紧性测度, 算子非紧性测度, Hilbert空间

Abstract:

In this paper, by using the classical Hausdorff measure of noncompactess theory, we study the measure of noncompactness of operators in Banach spaces (especially in Hilbert spaces); Specifically, we first give the representation of measure of noncompactness of operators in Banach spaces, and the equivalence of restricted measures in the whole space and subspaces; Finally, we study the equivalent properties of several semi-norms of bounded operator sequences between Hilbert spaces, especially including a kind of operator semi norm generated by Hausdorff measure of noncompactness.

Key words: Measure of noncompactness, Measure of noncompactness of operators, Hilbert space

中图分类号:

O177.92

沈钦锐,孙俊俊. Hilbert空间中的算子非紧性测度[J]. 数学物理学报, 2023, 43(4): 1003-1008.

Shen Qinrui,Sun Junjun. Measure of Non-Compactness of Operators in Hilbert Space[J]. Acta mathematica scientia,Series A, 2023, 43(4): 1003-1008.

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