Numerical radius inequalities for tensor product of operators

The two well-known numerical radius inequalities for the tensor product $A \otimes B$ acting on $\mathbb{H} \otimes \mathbb{K}$, where $A$ and $B$ are bounded linear operators defined on complex Hilbert spaces $\mathbb{H}$ and $\mathbb{K},$ respectively are, $\frac{1}{2} \|A\|\|B\| \leq w(A \otimes B) \leq \|A\|\|B\|$ and $w(A)w(B) \leq w(A \otimes B) \leq \min \{ w(A) \|B\|, w(B) \|A\| \}.$ In this article we develop new lower and upper bounds for the numerical radius $w(A \otimes B)$ of the tensor product $A \otimes B$ and study the equality conditions for those bounds.