Numerical radius inequalities for tensor product of operators

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