Numerical radius in Hilbert C✻-modules

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2021-01-12 DOI:10.7153/mia-2021-24-71

A. Zamani

引用次数: 4

Abstract

. Utilizing the linking algebra of a Hilbert C ∗ -module (cid:2) V , (cid:3)·(cid:3) (cid:3) , we introduce Ω ( x ) as a de ﬁ nition of numerical radius for an element x ∈ V and then show that Ω ( · ) is a norm on V such that 12 (cid:3) x (cid:3) (cid:2) Ω ( x ) (cid:2) (cid:3) x (cid:3) . In addition, we obtain an equivalent condition for Ω ( x ) = 12 (cid:3) x (cid:3) . Moreover, we present a re ﬁ nement of the triangle inequality for the norm Ω ( · ) . Some other related results are also discussed.

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数值半径在希尔伯特C -模块

．利用Hilbert C * -模(cid:2) V， (cid:3)·(cid:3) (cid:3) (cid:3)的连接代数，引入Ω (x)作为元素x∈V的数值半径的定义，并证明Ω(·)是V上的范数，使得12 (cid:3) x (cid:3) (cid:2) Ω (x) (cid:2) (cid:3) x (cid:3)。此外，我们还得到了Ω (x) = 12 (cid:3) x (cid:3)的等价条件。此外，我们给出了对模Ω(·)的三角不等式的重新定义。本文还讨论了其他一些相关结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.