Refinements of A-numerical radius inequalities and their applications

Abstract

We present sharp lower bounds for the A-numerical radius of semi-Hilbertian space operators. We also present an upper bound. Further we compute new upper bounds for the $B$-numerical radius of $2\times 2$ operator matrices where $B=\text{diag}(A,A)$, $A$ being a positive operator. As an application of the A-numerical radius inequalities, we obtain a bound for the zeros of a polynomial which is quite a bit improvement of some famous existing bounds for the zeros of polynomials.

arXiv comment13 pages

References in corpus (3)

• Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces
• Numerical radius inequalities and its applications in estimation of zeros of polynomials
• Numerical radius inequalities of operator matrices with applications

Cited by in corpus (6)

• $A$-Numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications
• Generalized $A$-numerical radius of operators and related inequalities
• Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
• Refinements of generalized Euclidean operator radius inequalities of 2-tuple operators
• $A$-numerical radius : New inequalities and characterization of equalities
• Improvement of $A$-numerical radius inequalities of semi-Hilbertian space operators