Numerical radius bounds for certain operators

被引：5
作者：
Bhunia, Pintu [1 ]
机构：
[1] Indian Inst Sci, Dept Math, Bengaluru 560012, Karnataka, India
来源：
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2024年
关键词：
Numerical radius; Usual operator norm; A-numerical radius; A-operator seminorm; A-adjoint operator; Positive operator; INEQUALITIES;
D O I：
10.1007/s13226-024-00663-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We provide sharp bounds for the numerical radius of bounded linear operators defined on a complex Hilbert space. We also provide sharp bounds for the numerical radius of A(alpha)XB(1-alpha), A(alpha)XB(alpha) and the Heinz means of operators, where A, B, X are bounded linear operators with A, B >= 0 and 0 <= alpha <= 1. Further, we study the A-numerical radius inequalities for semi-Hilbertian space operators. We prove that w(A)(T) <= (1 - 1/2(n-1))1/n & Vert;T & Vert;(A) when AT(n )= 0 for some least positive integer n. Some equalities for the A-numerical radius inequalities are also studied.
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页数：13
相关论文
共 32 条
[1]   Partial isometries in semi-Hilbertian spaces [J].
Arias, M. Laura ;
Corach, Gustavo ;
Gonzalez, M. Celeste .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (07) :1460-1475
[2]  
Baklouti H, 2020, LINEAR MULTILINEAR A, V68, P845, DOI 10.1080/03081087.2019.1593925
[3]   Joint numerical ranges of operators in semi-Hilbertian spaces [J].
Baklouti, Hamadi ;
Feki, Kais ;
Ahmed, Ould Ahmed Mahmoud Sid .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 555 :266-284
[4]   Notes on matrix arithmetic-geometric mean inequalities [J].
Bhatia, R ;
Kittaneh, F .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 308 (1-3) :203-211
[5]  
Bhunia P., 2022, Infosys Science Foundation Series in Mathematical Sciences
[6]  
Bhunia P, 2024, ARCH MATH, DOI 10.1007/s00013-024-02017-6
[7]   Numerical radius and spectral radius inequalities with an estimation for roots of a polynomial [J].
Bhunia, Pintu .
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2025, 56 (02) :830-840
[8]   Improved bounds for the numerical radius via polar decomposition of operators [J].
Bhunia, Pintu .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2024, 683 :31-45
[9]   Anderson?s theorem and A-spectral radius bounds for semi-Hilbertian space operators [J].
Bhunia, Pintu ;
Kittaneh, Fuad ;
Paul, Kallol ;
Sen, Anirban .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2023, 657 :147-162
[10]   Generalized A-Numerical Radius of Operators and Related Inequalities [J].
Bhunia, Pintu ;
Feki, Kais ;
Paul, Kallol .
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2022, 48 (06) :3883-3907
1234