On inequalities for A-numerical radius of operators

Abstract

Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in [A. Zamani, A-Numerical radius inequalities for semi-Hilbertian space operators, Linear Algebra Appl. 578 (2019) 159-183]. We also obtain some inequalities for $B$-numerical radius of $2\times 2$ operator matrices where $B$ is the $2\times 2$ diagonal operator matrix whose diagonal entries are $A$. Further we obtain upper bounds for $A$-numerical radius for product of operators which improve on the existing bounds.

16 pages

Cited by in corpus (14)

• Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces
• Bounds for zeros of a polynomial using numerical radius of Hilbertian space operators
• Generalized $A$-numerical radius of operators and related inequalities
• Some numerical radius inequalities for semi-Hilbert space operators
• Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
• On A-numerical radius inequalities for $2\times 2$ operator matrices
• Some improvements of numerical radius inequalities of operators and operator matrices
• The generalized Schwarz inequality for semi-Hilbertian space operators and Some $A$-numerical radius inequalities
• Further inequalities for the $\mathbb{A}$-numerical radius of certain $2\times 2$ operator matrices
• New semi-norm of semi-Hilbertian space operators and its application
• Improved inequalities related to the $A$-numerical radius for commutators of operators
• $A$-numerical radius : New inequalities and characterization of equalities
• Further improvements of generalized numerical radius inequalities for Hilbert space operators
• Some upper bounds for the $\mathbb{A}$-numerical radius of $2\times 2$ block matrices