Numerical radius inequalities for tensor product of operators

Abstract

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, $\frac{1}{2}\Vert A\Vert \Vert B\Vert \le w(A\otimes B)\le \Vert A\Vert \Vert B\Vert$ and $w(A)w(B)\le w(A\otimes B)\le \min \{w(A)\Vert B\Vert ,w(B)\Vert A\Vert \}.$ 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.

10 pages

References in corpus (1)

• Development of inequality and characterization of equality conditions for the numerical radius

Cited by in corpus (1)

• Numerical radius and ${\ell }_p$ operator norm of Kronecker products and Schur powers: inequalities and equalities