Some improvements of numerical radius inequalities of operators and operator matrices

Abstract

We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of $n\times n$ operator matrices by using non-negative continuous functions on $[0,\infty )$. We also obtain some upper and lower bounds for the $B$-numerical radius of operator matrices, where $B$ is the diagonal operator matrix whose each diagonal entry is a positive operator $A.$ We show that these bounds generalize and improve on the existing bounds.

19 pages

References in corpus (3)

• Numerical radius inequalities and its applications in estimation of zeros of polynomials
• On inequalities for A-numerical radius of operators
• Bounds of numerical radius of bounded linear operator using $t$-Aluthge transform

Cited by in corpus (2)

• $A$-Numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications
• On A-numerical radius inequalities for $2\times 2$ operator matrices