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

Some improvements of numerical radius inequalities of operators and operator matrices