Some improvements of numerical radius inequalities of operators and operator matrices

Pintu Bhunia, Kallol Paul

Published 2019-10-15Version 1

We obtain upper bounds for the numerical radius of 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 $B$-numerical radius of operator matrices where $B$ is the operator diagonal matrix with diagonal entries are positive operator $A$, and show that these bounds generalize and improve on the existing bounds.