关于重核Hilbert空间算子和Berezin-Radius不等式空间上的一个新范数

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2023-06-14 DOI:10.1080/01630563.2023.2221857

Pintu Bhunia, M. Gürdal, K. Paul, A. Sen, R. Tapdigoglu

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引用次数: 1

摘要

摘要本文给出了在再现核Hilbert空间上定义的所有有界线性算子空间上的一个新范数(α-Berezin范数)，它推广了Berezin半径和Berezin范数。研究了α-Berezin范数的基本性质，给出了涉及α-Berezin范数的各种不等式。利用这些不等式，我们得到了有界线性算子的Berezin半径的各种边界，改进了先前的边界。进一步，我们得到了算子积和的Berezin半径不等式，并由此导出了新的Berezin半径界。

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On a New Norm on the Space of Reproducing Kernel Hilbert Space Operators and Berezin Radius Inequalities

Abstract In this paper, we provide a new norm(α-Berezin norm) on the space of all bounded linear operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin radius and the Berezin norm. We study the basic properties of the α-Berezin norm and develop various inequalities involving the α-Berezin norm. By using the inequalities we obtain various bounds for the Berezin radius of bounded linear operators, which improve on the earlier bounds. Further, we obtain a Berezin radius inequality for the sum of the product of operators, from which we derive new Berezin radius bounds.

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来源期刊

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.