数学季刊 >

2016 , Vol. 31 >Issue 1: 39 - 43

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.01.005

关于多个算子形式的Bohr不等式

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  • Faculty of Light Industry and Energy, Shaanxi University of Science and Technology.  College of Electrical and Information Engineering, Shaanxi University of Science and Technology
LIAN Tie-yan(1978-), female, native of Weinan, Shaanxi, a lecturer of Shaanxi University of Science and Technology, M.S.D., engages in operator theory.

收稿日期: 2014-09-24

  网络出版日期: 2020-11-12

基金资助

Supported by the Key Scientific and Technological Innovation Team Project in Shaanxi Province(2014KCT-15)；

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Bohr Inequality for Multiple Operators

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  • Faculty of Light Industry and Energy, Shaanxi University of Science and Technology.  College of Electrical and Information Engineering, Shaanxi University of Science and Technology
LIAN Tie-yan(1978-), female, native of Weinan, Shaanxi, a lecturer of Shaanxi University of Science and Technology, M.S.D., engages in operator theory.

Received date: 2014-09-24

  Online published: 2020-11-12

Supported by

Supported by the Key Scientific and Technological Innovation Team Project in Shaanxi Province(2014KCT-15)；

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摘要

An absolute value equation is established for linear combinations of two operators.When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in literature [3] and its equivalent deformation are obtained.Based on the equivalent deformation of the operator equation and using the properties of conjugate number as well as the operator, an absolute value identity of multiple operators is given by means of mathematical induction. As Corollaries, Bohr inequalities are extended to multiple operators and some related inequalities are reduced to, such as inequalities in [2]and [3]. 

关键词： Bohr inequality; absolute value operator; adjoint operator; mathematical induction

本文引用格式

连铁艳 , 汤伟 . 关于多个算子形式的Bohr不等式[J]. 数学季刊, 2016 , 31(1) : 39 -43 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.01.005

Abstract

An absolute value equation is established for linear combinations of two operators.When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in literature [3] and its equivalent deformation are obtained.Based on the equivalent deformation of the operator equation and using the properties of conjugate number as well as the operator, an absolute value identity of multiple operators is given by means of mathematical induction. As Corollaries, Bohr inequalities are extended to multiple operators and some related inequalities are reduced to, such as inequalities in [2]and [3]. 

Key words： Bohr inequality; absolute value operator; adjoint operator; mathematical induction

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